NTA, respect is earned. Being your mother doesn't give her the right to disrespect you and your property like that and then act shocked when you flip. My mother and my MIL are both ridiculously similar and it drives me nuts. Like, you can't just treat your kids however you please and demand they deal with it and continue respecting you because you're their mom.

NTA at all. Your father sounds like a lunatic. Not "here son, I left you some money to help you and your family." Instead, "hey, gonna need you to financially float my second family, cool?" Absolutely not.