These family of origin members seem to ignore the fact that their darling son or daughter is going along with the spouse's supposed "program." Maybe they are just weak-minded souls who are easily led by the nose? Not!
Anyway, for many of those dads who seem to want to avoid the kids from their "first" family, their new wife volunteers to be the villainess, just as she might have done with dad's estranged parents. She makes it look like Dad's avoidance of the children is entirely her doing. This way, the abandoned kids get to feel better about their dads by blaming his absences on his mean and nasty new wife.
In a way, she is actually trying to protect the abandoned children from the pain of being seemingly rejected by their own fathers.