what about in a continuing, viable marriage... where the Husband/Father resigns, and wants the children (say, under 15 y.o.) OUT, but the mother doesn't?
Would LDS, Inc. still recognize him/his wishes as 'the Head of the Family-Household' ? there's a question fer ya...
I've talked to and read dozens of cases. Mormons try to follow commandments but building the kingdom is more important to them than rules or procedures.
Legally if both parents have custody with no official record of separation or divorce, only one of them has to be there for any legal application, i.e., a passport, registering for school, admittance to a treatment program, etc. This means that one parent can request resignation for minors and the other can get them re-baptised. It's a messy situation; the law doesn't cover differing views on religion in an ongoing marriage.
If you're officially separated or divorced, it's a whole different ball game. Most legal decrees in these cases require the permission of both parents for anything of significance.