To truly answer this question, I would need to know more about the persons involved in each situation, particularly the one resisting, but to understand what is going on it would be important to understand the motives involved in the persons, their choices and actions. So, let's suppose that the one "stubbornly refusing to accept a vocation" is doing so while knowing it is a call from God. And let's also suppose that the second person loves her family and respects their perspective on things and also loves God and his Church; in answering this call she is being faithful to herself and her love of God.
When set up this way, the difference between the two situations looks to me like that between someone who accepts a call to authentic humanity in obedience to God and someone who does not. They do this despite the pain linked to the insecurity of the calling it apparently causes their family because, while loving their family, they trust God's wisdom in calling them to this vocation. Moreover, they might be said to believe the judgment that this vocation is "not viable" is the word of a world that values things differently than a Christian does. What is important in Christianity, you already understand, is the countercultural, but it must be chosen for the sake of the Kingdom of God, even if that means a lack of viability in the way this world might deem such matters. (Jesus' choice of integrity in the face of Roman power was countercultural, and it was countercultural for the sake of his Abba's sovereignty in this world. The picture could change completely if the motives of the individuals given, were different from the ones I have supposed. For instance, if the person insisting on responding to a call to a non-viable situation was motivated by rebellion or by a need to stick it to her family, and wanted to do that come what may, the situation would be radically different, wouldn't it?) I hope this is at least close to what you were asking for.
2) In your experience do the most recent Church directives for contemplative nuns (9 - 12 years of formation and becoming part of federations and associations) have any implications for hermits - especially as regards writing their rule of life?]]
While these directives don't have direct application, yes, I believe they do have implications for hermits, particularly in the writing of a Rule, just as you suggest. Part of formation is becoming capable or being made capable of engaging in formation for the rest of one's life. Discernment is a huge part of this so one has to learn how to discern the will of God in a mature way as a solitary consecrated hermit so that one may continue doing so and thus, being formed in this life, over the rest of one's life. That requires significant swaths of time. Cor Orans has good sections on various stages of formation and the section on initial formation is where the 9-12 years comes from. I would say that all of the general comments on the nature of formation here (that it is integral, that growth is organic, that there is a need for consistency and coherence, and that it involves significant initiative from the individual nun) all apply to eremitical life, yes.
As regards the writing of a Rule, one must have acquired the experience and correlative expertise that allows one to write such a document. This is one of the reasons it is necessary to live religious life and/or as a non-canonical hermit for some time before petitioning to be admitted to profession under c 603. Further, ongoing spiritual direction contributes to the kind of habits of self-reflection necessary if one is to write a Rule that combines, 1) the way God has worked in one's life, 2) the central elements of canon 603 itself, and 3) the redemptive experience that is at the heart of any authentic call to solitary eremitical life. While a chancery might not want to commit a small team to work with an individual re discernment and formation as a c 603 hermit for upwards of 9-12 years, such a period associated with pre-profession formation and the formation associated with temporary profession is not inappropriate. That is especially true given the emphasis texts like Cor Orans and Vultum Dei Quarrere place on the importance of the contemplative nun taking responsibility for her own growth/formation, as well as the possibility of mentoring by other c 603 hermits assisting the diocesan team and the individual hermit.
3) What are your thoughts about some more recent spiritual families such as the Monastic Family of Jerusalem, the spiritual communities inspired by the life of Charles de Foucauld, and the Carmelite Secular Institute of Notre Dame de Vie (Our Lady of Life)? Are there viable eremitic or semi-eremitic elements in their lifestyle?
I am sorry, but I am not especially familiar with these groups. I know there are almost two dozen individual groups now associated with the Charles de Foucauld "Family", but apart from several of the names I just don't know enough about them to answer your questions regarding viable eremitic or semi-eremitic elements. Regarding the Carmelite Secular Institute of Notre Dame de Vie, what I do know of it is that its members work full-time and devote 2 hours a day to private prayer. While that is certainly commendable it doesn't rise to the level of eremitical life, not only in terms of prayer, but also given the degree of work built into a day and week. For that reason, my answer to this portion of your question would need to be no, I don't see viable eremitic elements. By the way, when I use the term semi-eremitic, I do not mean half-hermit, but rather eremitical life lived within a communal context that is meant to foster the life of the hermit. The Carthusians are semi-eremitical in this sense.
4) What happens when a laura or association of hermits dies out, or at least the founder/foundresses die and/or the laura/association disbands? Is continuity a valid concern for hermits?
If the laura is formed of hermits who were professed and consecrated under c 603, the dissolution or suppression of the laura would not affect the canonical standing of the remaining hermits. With regard to c 603 hermits, lauras are allowed for the sake of the solitary hermits' spiritual and physical (or perhaps material) support. They are not to rise to the level of a juridical community (common purse, common superior, common Rule, etc.), however, and are not houses of formation. The individual hermits who come together in this way are already professed as solitary hermits with their own Rule and all of the obligations and rights associated with c 603 standing in law; for this reason, the dissolution of the laura does not constitute a material change in the context or content of the vows themselves. (Vows are made as solitary hermits, not as members of a laura.) Yes, continuity is very important for a hermit. I would argue that c 603 itself, especially in its requirement that one write a liveable Rule of Life and the vocation's diocesan focus as well as the basic fact of its public nature**, provides the continuity necessary for a solitary hermit whether they live this life in a laura or outside of it; it provides an ecclesial identity and a stable state of life within which one may seek and achieve genuine sanctity and/or fullness of humanity.
5) Is there still a place in the Church for extremely small groups of 3-5 people living eremitic or semi-eremitic life?
I should think so! Most of the time c 603 hermits live alone and come together via ZOOM, for instance, in what might come to constitute virtual lauras. However, I know of one 3-member group of hermits in the mid-west and another (unfortunately now down to just one Sister) in Idaho which seems to indicate they are still open to receiving new members. I recently worked with a priest who was temporary professed under c 603 and who was from another laura of perhaps 5 or six members (though he eventually moved on to the Monte Corona Camaldolese to try his vocation there). So yes, it is possible and still happening. One mistake I have seen bishops make with such arrangements, however, is to require one join the laura if one wants to be professed under c 603. This, it seems to me, has the cart before the horse -- as I described briefly above. But yes, there is no reason 3-5 individuals could not come together to live eremitical life so long as the property and living arrangements allowed for and supported significant silence and solitude for all involved.
** Remember that "public nature" here means "a vocation with a commitment involving public rights and obligations." It does not mean public in the sense of notoriety or being seen by or accessible to everyone. Even complete recluses may have public vocations and provide public witness simply by being known as a recluse.