I tell my children that, should they choose to marry, they must marry a traditional Catholic for there is no bishop with ordinary jurisdiction available to them (at this time) to give dispensation for any marriage that would require a dispensation.

I don't know if any traditional bishops attempt to give dispensations, but the fact is that they don't have the legal authority, even under the extraordinary circuмstances in which we find ourselves today, to give dispensations to baptized Catholic faithful who wish to marry.  

I know one particular independent traditional priest who would not marry a couple until the man converted and he, the priest, was sure the man as truly convinced of the truth of the Catholic faith.  The priest said he had not the authority to marry them in the Church.  To my knowledge, this couple never did marry and the man eventually abandoned any pretense of even learning the Catholic faith.  (N.B.:  I doubt this would have been a successful marriage and had they had children, the family would have not remained Catholic.  This is the problem with mixed marriages.)

As to the question of how traditional clergy deal with couples who, having been illegally married (according to Church law) or given dispensations by Conciliar bishops and later find the traditional Church, I really don't know.  Somehow, I think such should probably be treated as converts would have been treated in the early Church.  Past irregularities are probably dealt with in the confessional while potential irregularities would be disallowed.

This may be a burden for some, but it is a burden that will ultimately be better for all concerned.  The Conciliar church, having completely distorted the ends of marriage (even to the point in which the current Conciliar pope supports legal marriage of sodomites as long as the title of their disgusting union is called something else, i.e., "civil unions"), is unable even to understand the purpose of dispensations let alone give them for honorable reasons.  They don't know how to marry anyone so they are willing to dissolve virtually all marriages as well.

Marrying a traditional catholic is the best option. Mind you, it can be problematic finding one.

Traditional Catholic bishops don't have jurisdiction, which is required for the binding and loosing of laws (in this case, the precept against mixed marriages) so it's a moot point.