This is an interesting and hard dilemma OP, and so hard without that crystal ball!
2 things that strike me though in your original post:
Her piano teacher thinks she's great and constantly tells me how good her musical memory is and how she could go all the way
As lovely as this is, could it have placed a lot of pressure on your DD, albeit inadvertently? There are lots of kids out there that do have a natural talent for something, but have no wish to take it all the way
(the only thing she really shines at)
This is so tricky with DC in your DD's age group, but 13 is still early to define what she is good at. There may be other strengths that just have not come to the fore yet. Your DD clearly has talent for music, and whilst there are many unwelcome influences at this age, I don't think forcing her will help long term. I absolutely agree with drummers in trying a completely different tack and suggesting completely alternative music genres to the usual classical approach. Even if it's total popular music only (that you hate)! if it keeps her ticking over until she finds the love again, then great.
Ultimately, she has reached a competent level. Not to become a concert pianist but has all the platform basics. And may wise up further into her GCSE music syllabus and want to return to piano in a properly. Though even writing that sounds wrong, as 'properly' is so subjective and restrictive (and really parent centric!). Y10 is a big jump from Y8/9 in maturity terms. Her choice and decision then, resulting in hopefully, a more productive relationship with her instrument/new teacher - and she's in control of her choice.