A, I find it extremely odd that your h has organized a birthday part for his mother on the last day of August. Like you pointed out...she's 73 years old. Unless, of course, he feels guilty for neglecting her over the years and thinks she's likely to pass away in the next year. That is so strange! I feel for your daughter and I don't blame her. I wouldn't want to go to a party and not have anyone my own age there. Yes, she's right...she would be expected to look after the little ones. That so ruins the fun of attending such events.
Yes, the op are very manipulating and know just what buttons to push to become the "cream of the crop" w/the parents of the walkaway spouses. Such a shame that they can't see the light of day for what they are all about.
If your h does come by to pick your daughter, stay up in your room and/or another part of the house. You do not need to be mistreated by him.
Please take care of yourself.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.