Wow your stepdaughter sounds like a nightmare, I feel so sorry for you.
I think the invitation should still be extended to her due to her age, but all the choices should be on your/DH terms. Eg spending money, where you go.
She should be treated the same as her brother/s and not given a huge wardrobe allowance just for being the only girl.
I don’t think a whole set of new clothes are needed each holiday, I certainly never expected that. At 15 if she is still growing and needs larger sizes, sure. But most 15yo girls are not going up sizes every year anymore. Maybe give her a budget (£100?) that is the same as the other children to spend, and she can choose whether that is on vinted or primary or Canada goose.
If she doesn’t want to talk to you, don’t bother trying to talk to her. Just keep offering to let her join family activities and leave it at that. She’s not your responsibility to raise into a considerate pleasant adult, the boat has sailed for that.
Once she is 18, you don’t need to invite her to family holidays anymore.
She will still find things to moan about, so just leave her to it.