Things are tough in a divorce and it is a large cause of poverty. It is likely impossible to sort things out here, and one thing might be that your dad is stretching the truth. Perhaps he paid half the bills some months, but not all. It could also be that he did pay half all months, and your mom is a poor money manager. Budgeting and living within one's ...
I wouldn't call it an impediment but you need to have a written mortgage agreement in place to identify at least the following terms:
Monthly payment amount and due date
What happens if you miss payments (i.e. at what point are you in default and they foreclose)
What happens if they die
What happens if you die