Have been both the 15yo & SM.
As some may say, you have a DP problem.
Most of all, SD needs her father’s time, interest & affection. That is time spent just the two of them hanging out, maybe a hobby, going to the movies, pottering about at home, making brunch for everyone, going to buy her an outfit on a fixed budget. This when the everyday sharing of everyday concerns, hopes & dreams are shared. When his DD knows in her bones that her father is there for here as she grows up.
Forthcoming holiday: yes she goes with you, accept her affected indifference with humour, give her a gift card for her favourite shop with fixed amount for her to buy a holiday outfit.
It’s important that she’s included, gets to know her extended family.
If she steps badly out of line, tell her off as you would your own.
In times to come she may be the person who makes all the difference with her siblings, I.e. your children.