Would the children be sinful for refusing their father's return to their home after a long absence and neglect of them, and for supporting their mother, who does not wish for his return?

The rights of parents are great, so it is not permissible to return their bad treatment with similar treatment. Rather, one must treat them with kindness, even if they fall short in their duties. As for the father's presence with his son at the engagement, if his presence would lead to corruption, then there is no harm in going without him. Otherwise, preventing him is an act of disobedience. As for the father residing in the house, if the house belongs to him, then preventing him is forbidden. But if it belongs to you, then preventing him without a reason is an act of disobedience that is not permissible.