N.S.
I AM a stepmom, so maybe I can help.
Blended families aren't easy. Boy, they can be hard! And It's so hard to have another mother-figure in your daughter's life.
As far as being a stepmom, the level of involvement depends on the agreements you make with your ex, and how much time your daughter spends at your ex's house. Also, communication has to be REALLY good.
I understand her wanting to help on her side when your daughter is with her. She is not your daughter's mom, but she is an adult figure at that house. I would NOT like if if I could not discipline a child in my own house, and it would make my husband feel very alone if he had to do everything. So I can understand that, provided that the discipline she uses is agreed upon by you all. For example, I take away the TV if my stepdaughter is not behaving, but I would never touch her even though my husband does do spankings.
As for the party, I could understand if she wanted to help throw a party on her weekend with her made up of your husbands relatives and perhaps her own and maybe some friends that your daughter knows that live near there. We do that.
BUT, she should not throw the main party, and of course should consult you first, especially if it's YOUR weekend with her and definitely should take a back seat if you're planning one party all together.
As a stepmom I do not consult the mom on every little thing I do, and it would be impossible to run the house and never do or say anything to discipline or encourage the child. If we decided to take her to the zoo on our weekend, do we need to call the mom and ask? Of course not. Do you consult the dad on every little thing?
It sounds like you just need to have a talk with your ex, no stepmom involved. Your daughter will have to get used to two sets of rules should they differ. 9pm may be too late for phone calls at your house, but 8pm may be the stepmom's rules. That's just how it's going to be.
The stepmom needs to learn her boundaries (and give her a little time to get used to it because it IS hard. Stepmoms want to play their small role in the child's life) but you also may need to let some things go. Your daughter has TWO women in her life. You will always be the mom, but the stepmom can be a friend too.