My mum gave me her old car when Dad got her a newer one (OW/Guilt gift, but that's something else)
I was 17. Living in the middle of nowhere. My allowance didn't cover the petrol, so guess what... I got a JOB.
Your DD has NO right to a thing from you, not after they strafed you of a house, I am utterly sick at that level of manipulation, she is doing her revolting father's dirty work.
Don't tell her about the holiday, don't get her a car, don't do a fucking thing for her.
She is CHOOSING to be vile to you, because she saw her dad do it, and she is taking it all out on you, blaming you for the split cos she's too frightened to talk to her dad about it, or she'd lose her glittery life.
Guess what? If her dad were not being dismissive of her, she'd STILL be entitled.
She needs to see how hard life is out there for normal people, and what you have been made to do for her.
You rent that house, you pay for it, you furnish it. YOU go to bed when you like and if she has a problem with that, TOUGH! Don't EVER allow anyone to treat you like this! Just because she is family? well IMO, family need to treat you BETTER than strangers. The bar is set higher.
I suggest that you stand your ground, but that when the time for Uni comes, that she goes and studies at one FAR away so that you can get your life back, and she will learn what life is really like.
You have not let her down love, she has let herself down. One day I hope she looks back and is utterly ashamed of herself.