It is possible that to inherit the house from the deceased parents, OP's parent had to payoff her sibling(s)' interest in the house. For example, if I were to inherit a $500,000 house from my parents, I would have to pay off my four siblings' interest in the home and would therefore need a mortgage of approximately $400,000.00.

"It is possible that to inherit the house from the deceased parents, OP's parent had to payoff her sibling(s)' interest in the house. " Only if the house was inherited by all the siblings. Anyway, my guess is that that's not the problem here; the OP emphasises how this house has been in the family for three generations. If the parents are paying out their siblings' share in the house, then if they 'lost' the house it'd still stay in the family by going to one of the other siblings. Unless the siblings forced the OP's parents to actually take out a mortgage to pay them up front, in which case they'd be pretty unsympathetic siblings.

Raising a small child, they probably can't afford to help pay a mortgage and pay rent for another home. Moving in they are helping to pay for the house and they don't have to pay rent somewhere else.

Not everyone has money to pay their own rent/mortgage AND lend money to pay someone else's mortgage. Edit - didn't see the above comment.