Before we got married, my late husband got phone calls from his ex for things like tyre punctures - her affair partner/boyfriend was pretty useless at that type of thing.
Part of it was a control issue, I'm fairly certain - particularly given other matters that happened after we married.
Less than a year after the the first boyfriend died, she had a new man who was good at handiwork. When he died, she had a new man less than a year later. (By then, my DH was very unwell following heart trouble and a stroke.)
You're stuck between a rock and a hard place, OP. I think you're maybe going to have to put up with it until your husband's daughter has left for uni. Then you can put your foot down.
So far as watching the kids so that she can get her nails done? Oh no... Sod that for a game of soldiers.
I was too understanding. DH's kids were adults, but I bent over backwards to be 'nice' so as not to rock the boat with regard to his relationship with them. I did stand up for myself in some respects. (I'll not take up more time listing some of the manipulative things the ex did.) We'd had a better relationship with the ex in some ways latterly - I even took her to hospital when she was between men, cos there was no sign of the kids doing it.
Result? After DH died - and the ex was with her FOURTH man - she was behaving as though she was the widow. It was as if I was some kind of junior wife. Bizarre.
I finally blew my top two months after the funeral..put my foot right in it. DH's kids and grandchild have gone No Contact. Haven't heard from them for nearly 4 years. (They were quick enough to cash the cheques they were sent for their inheritance and then a wedding and a graduation.)
As others have said, I'm guessing you'll have to agree to your DH doing things for his daughter...but his ex and the other two kids are not his responsibility.
If your husband can't agree, time to look at your options.
About a year after my husband's funeral (which happened during lockdown) I recall sobbing to a friend and saying that I felt like second-hand Rose. I know my husband loved me dearly...but the way that I was treated around the time of the funeral was dreadful.