Actually, everything you are saying is perfectly reasonable. At least, according to your rules. According to their rules, you're in the wrong. And, sadly, in their house, the rules are the rules that they set out.
With her father, you are never going to win, so don't try. He is accustomed to being the one who is in charge and to have another man arguing with him is only going to turn him against you. The mum is the one you really need on your side: ultimately she's the one who can sway the father.
However, it does seem like she's taking the piss. Anyone who says "You don't do anything for me" after a day of ferrying her around clearly doesn't appreciate what you do for her. Normally it would be best to just say "Well, here's a list of things I've done for you lately" but then she'd respond "OH! How undutiful a son in law you are! You keep a record of all these things, you think it's a chore to help me!"
Basically you don't win.
Question: do you pay rent?