[[1) Are there such things as "unworthy" crosses, or "unholy" crosses? 2) Is God only able to use "holy crosses", or "worthy crosses" in our lives?? 3) Does he simply remove these ["unworthy"] crosses for us??]]
Well, it's an interesting couple of questions, but the answer to the first one is no (or potentially so), and the answer to the second question is a definite no!! The third one is a bit more nuanced, so see below. Let me start with the second question, (Can God only use Holy crosses?) which is more straightforward, and more clearly theological. It will provide the basis for answering the first and third questions as well.
Jesus' Cross as Paradigmatic:
To begin we must start with the central paradigm and symbol of our faith, the Cross of Christ. When we think of the Cross of Christ and Christ's passion it is critically important to remember that what was most significant about it was not the agonizing physical torture associated with it, horrific as this was, but rather the shame, offensiveness, and scandal of the cross as these were judged by human beings. In terms of Jesus' culture and time there was nothing holy, or worthy, or respectable about the cross Jesus assumed as his own. Quite the contrary. It was in every way the cross formed and shaped from and by human sinfulness, depravity, cruelty, inhumanity, and shamefulness --- not from human nobility, compassion, integrity, or anything similar. This cross represented the antithesis of the holy, the good, or the noble. It was understood to represent Godlessness (anti-life, anti-holiness, etc.) in as absolute a way as anything could. And of course, it is THIS shameful, unholy cross that God uses to redeem and reconcile his entire creation!
With this in mind, I think I can now approach the answer to your first question. There is no doubt that many of the crosses that afflict our lives are the result of unworthy choices, whether our own or another's. Not all the crosses we are called to bear are the result of an unchosen illness, for instance. People hurt one another, sometimes deeply and in ways which leave wounds which are difficult to work with or treat. Children are abused by parents and their capacities to love, trust, or live can be badly impaired. Adults sin seriously and impair their own and others' physical and emotional health in the process. In so many ways we carry the scars of these events, sometimes for years and years, sometimes our whole lives long. When you refer to unworthy or unholy crosses I think you are probably referring to these kinds of things, crosses that are the result of sin, inhumanity, cruelty, and the like. They are not unworthy in and of themselves, but they are the result of choices which are unworthy of both God and mankind, so let me go with that understanding for the moment.
So, what are we to do with such crosses? And further, can God use these for his own purposes even if he does not "send them"? Well, as with any cross we are to bear them patiently and courageously. HOWEVER, to bear them in this way does not mean simply to carry on without treatment, therapy, necessary personal work, healing and the like. To bear these kinds of crosses REQUIRES we work to allow the healing we need to live and love fully as human beings. This correlative work is actually a piece of bearing our cross patiently and courageously, ironic or contradictory as that may initially sound.
Let me give you an example of what I mean. A child who is abused will grow up scarred; it is a cross she will have to bear for her whole life, though not necessarily always in the same way. However, it is a cross which will need to be borne precisely by taking on therapy and the hard work of healing. Were she to refuse this work and allowed her life to be dominated or defined completely by the past, she would not be embracing her cross or bearing it patiently, but denying and rejecting it. One does not embrace one's cross by refusing to live fully. To bear a cross patiently means to take on LIFE in its shadow, and marked by its weight and imprint and to do so with the grace of God which brings life out of death, wholeness out of brokenness, joy out of sorrow, and meaning out of senselessness. It does NOT mean to forego the challenges of living fully in the name of some piously-rationalized cowardice and "victimologization". For example, the abused person would not be bearing her cross patiently if she said, "Well, God sent this cross, so I will simply accept all the consequences, dysfunction, crippled human capacities, and distortions that come with it. Don't talk to me about therapy, or moving out of this abusive relationship, or working hard to change the situation, etc. This was God's will!"
Prescinding from the idea that God sent this cross for the moment (a notion which I personally reject), what this attitude describes instead is capitulation to what Paul calls the powers of sin and death which are so active in our world. It is the refusal to allow God to redeem the situation, the refusal to be free in the Christian sense; it represents the embracing of bondage or slavery instead. Whether witting or unwitting it is an act of collusion with the destructive effects and process of the cross. Whether one is motivated by cowardice, hopelessness, masochism, or some other similar motivation, in this case the pious sounding, "God sent this cross so I will accept it, all its consequences, dysfunction,. . ." is a refusal to live fully, a failure to seek or embrace the call to genuine holiness and humanity which is one's birthright. It is a refusal of God's grace as it usually comes to us as well, for in such a situation God's grace ordinarily comes to us through things like the processes of therapy, spiritual direction, personal work, and all the relationships and changes which bring hard won healing and wholeness.
Can God Use the Crosses that Come to Us?
Can God use these "unworthy" crosses for his purposes? Of course. Why would he not be able to? To suggest otherwise is to say that God is incapable of redeeming certain aspects of his creation, or of making all things work for good in those who love him or let him love them. It is to suggest the Christ Event was a failure, and today's passage from Romans 8 (nothing in heaven or on earth can separate us from the love of God) is hyperbole at best, and a lie at worst. God may not have sent this cross, but there is no doubt that he can use it as a unique source of grace in one's life. We grow in all kinds of ways when we embrace the unavoidable difficulties life throws our way, but especially when we do so in faith and in concert with God's grace. This points up another way of refusing to carry one's cross, an unusual way I think, but a refusal nonetheless.
It is a refusal to carry one's cross to say, "God did not send it, so let's just be rid of it (or ignore it, etc). I cannot grow in this virtue or that one in light of this cross because it is unworthy, unholy, and God did not send it." In fact, God ordinarily does NOT send the crosses that come our way. They are forged instead in the workshops of human sin, illness, stupidity, cruelty, venality, and violence --- just as Jesus' cross was. And yet, God expects us to take them on with his grace so that he might redeem us and our world. I don't for an instant believe that God sent chronic illness, injury and pain for me to live with, however, with my cooperation he can use these to transform both me and my world. I don't for an instant believe that God sends the crosses that are the result of abuse, neglect, carelessness, cruelty and the like, but there is no doubt that he can use these to transform their sufferers and our world.
Could God Just Remove our Crosses?
Your last question was a bit more of a surprise than the other two and you may need to say more about it for me to answer adequately. Let me take a stab at it though. Does God simply remove these crosses for us? My first answer is no, though I am sure he COULD do. My second or related response is a question, "why should he?" I suppose in some way this question stems from your other two: if a cross is unholy and unworthy and God did not send it, then why shouldn't he simply remove it? But the simple fact is that crosses become holy and worthy in the bearing of them! They are "worthy" or "holy" crosses only when the one afflicted by them bears them worthily and in holiness. These crosses become something other than the result of human sinfulness and cruelty when they are borne with grace --- and here grace does not simply mean superficial equanimity (or something less noble like grudging resignation!); it means our "humble openness to the life-giving power of God's accompanying love with and through which we embrace healing and wholeness, holiness and fullness of life." Similarly WE become holy as we bear these crosses because in bearing them we become persons defined by the grace of God.
God has chosen to redeem this world by participating in its crosses, but as with Jesus, that means that one has to take the cross on in a conscious way and walk with it. Of course we will fall under its weight from time to time. Jesus did as well. But even though he could not see the future results he remained open to what God would bring out of it all. This is why Paul's summaries of Jesus' achievement focus not on his pain but on his obedience: "Jesus was obedient (open to God) unto death, even death on a cross." In the end, it is only in this way that God can take on sin and death, enter into them exhaustively, and transform them with his presence. He must be allowed to touch them with his compassion and Life. We take these things on, we embrace the crosses life brings our way as a part of Jesus' own redemptive work --- a share of his ministry of reconciliation; we cannot eschew such a burden and be true to our callings because at bottom our vocations always mean being the recipients, bearers, and mediators of God's transformative love in Christ.
Distinguishing Between Worthy and Unworthy Crosses?
Theologically, it makes no sense to me to try and distinguish between those crosses which are sent by God and are worthy of being borne, and those which are not. Partly that is because I don't believe God sends crosses so much as he sends the means by which they may be redeemed and become redemptive. Partly it is because it is precisely the unholy and unworthy that God takes on WITH US (and in us!) transforming them into something of value and holiness. Did God send Jesus the cross he took on! NO, it was entirely a human construct made with our own bloody hands and twisted, frightened hearts, but absolutely he sent Jesus into our world to TAKE IT ON! Do you hear the difference? Does he send us the crosses that come our way? No, but he sends us into the world so that we might be part of its redemption and fulfillment; that means he sends us into the world to take on the various crosses that COME OUR WAY "naturally" (and by "naturally" I mean that come our way through the human sinfulness, illness, cruelty, and violence we meet everyday.
Summary:
No cross is worthy or holy until it is borne with grace and courage. God does not send crosses per se, but he sends us into a world full of them expecting to help us in their redemption, and he certainly commissions us to carry the crosses that come our way. The only other point that needs to be reiterated is that we bear crosses patiently only when we choose to live fully in spite of them and by taking them on with the grace of God accompanying and empowering us at every step, faltering or not.
That means we take on the therapy, medical care (including appropriate medications for pain, etc), personal work of healing, and so forth that are part of these crosses. If someone has hurt us, even if they have hurt us very badly, it also means taking on the work and the PROCESS of healing which leads to genuine forgiveness. This can take years and years of course; it is not simply an act of will even though it involves such acts (often innumerable acts of the will in renewed intentions to let the crippling past go and live fully in the present). It requires assistance, not only of God, but physicians, psychologists, confessors, spiritual directors, and friends. The bottom line is there are many ways to refuse to carry a cross including by labelling them unworthy or unholy and waiting for God to simply remove them; to carry them means more than simply accepting the events that forged them initially; it means accepting --- and more, embracing everything necessary to transform and redeem them and ourselves as their bearers as well. Ultimately it means trusting that God is the one who brings good out of all things; it means trusting the One whose Love makes whole and holy as He weaves a tapestry of grace, beauty, and meaning from the awesome threads of potential we each carry along with our wounds and scars.