My understanding, FWIW, is that where the Catholic Church was the legal authority for marriages, there the children were legally illegitimate, which would affect things like titles, inheritances, etc.
But more and more there is a distinction between marriage as the state understands it, where annulment would be quite rare (Hey! They're brother and sister! They can't be married!) but where other legal requirements might arise concerning care and inheritance and all that and, on the other hand, marriage as the Church understands it, where a defective intention would be a good reason to say the marriage never happened. (That sentence long enough for you?)
As an example of a defective intention, I would suggest -- just suggest -- a pre-nup that contemplates who gets what if the couple divorces. My thinking is that if the couple is not ready to go for broke, to risk everything to keep their vows, then they don't intend matrimony. So a pre-nup that contemplated divorce would be a good reason (to me) to say a sacramental marriage never happened,because the couple did not intend what we mean by marriage.
DOes that make any sense at all?