AW, HECK NO!!!!
That is beyond ridiculous. I have learned (through experience) that my hours are my hours for a reason. I have set my hours based on what MY FAMILY needs, and then based on what the client's needs are. Not the other way around. I would also have her dressed and ready at the door from 6:00 on. If you need to leave her coat off, so she doesn't get too hot, that works too. But I would sit by the door/entry and read stories or do puzzles with her. When mom arrives, put the coat on and hand her over, saying "Goodnight, see you tomorrow!" And then, literally close the door in her face if need be. That may seem rude, but her sitting at your table, staying insanely late and eating your food (I don't even care if she DID ask permission) trespasses over a lot of social boundaries.
If you don't stop this now, you know it will only get worse.