I think you’ve had great advice here and I also think that the only way to turn it around for yourself is as others have said - is to emotionally detach/disengage from her.
It sounds like a really odd concept but at the end of the day, if you are becoming so low, it’s your best option, otherwise you’ll likely slip into depression. You can’t change her and if your partner is unwilling to confront her behaviour head-on, this leaves you few options other than to leave the relationship or to detach from her.
In my personal experience of going through this myself, I left the relationship, I left because I was being scapegoated by everyone including my partner, detachment wouldn’t have worked in my situation but if everything is pretty good otherwise for you, then you do not need to leave the relationship with him, you just emotionally leave the relationship with her.
As others have suggested, you also stop doing all the nice things you’ve been doing for her and essentially hand over all responsibility to her father. So if her bed isn’t changed or made and he doesn’t do it, it gets left. If her clothes are still on the bedroom floor where she left them and he hasn’t washed them, they get left there.
I think there is a difference in being petty and detaching though. For example, if her clothes are in the dirty laundry basket with other people’s stuff, don’t be so petty as to wash everything else and leave hers out, your partner will pick up on these sorts of things and that of course has the propensity to fuel arguments and resentment between you.
I would also suggest that when she is being nasty or ignoring you in the presence of your partner, that you do not do the most instinctive thing of removing yourself to another room or out of the house, but that you make a fuss of him. So you go over and give him a kiss on the cheek or a cuddle or a great big smile.
Your SD will soon start learning that her petulant and spiteful behaviour towards you, will not see you out of her father’s life nor out of his love for you.
So don’t let this insecure human-being drag you to your knees, she is 15 and will no doubt be sidelined in a few years time with boyfriends and college and friendship circles.
Hang on in there and good luck!