At 13 you can’t force her to go but I would try to get to the bottom of why she doesn’t want to.
Is she generally a self harmer or is she just threatening to do so because of this? Because tbh that in itself is pretty manipulative of her, and without her being able to explain her reasons, threatening self harm because she doesn’t get what she wants is something I would tread carefully with before just blindly accepting it.
Also while she can choose not to go and stay there, she should still be encouraged to at least maintain some contact with him, unless there is outright abuse in the equation. At 13 she is old enough to decide not to see her father, but too young to realise the potential long term implications of not doing so.
My DS stopped staying at his dad’s when he was 14, but that was due to issues with his dad’s partner, and eXH siding with her over him. Before that he was reluctant, but I always encouraged, and tbh when he was there he ended up having a good time.
But after he stopped staying there i never discouraged contact with his father, never encouraged him to not have a relationship with him, and while I listened to his reasons, I acknowledged them but didn’t indulge them.
Because it’s always important to remember that children will give you the side of the story which benefits them the most.
Going forward eXH maintained a relationship with DS away from home. They have been away on a couple of trips, they go out to dinner occasionally, and DS is now an adult, and while he doesn’t have a close relationship with his dad, even he is grateful that I never blindly encouraged him to stop contact.
As a parent you need to have your DD’s back but you also need to be able to play devil’s advocate sometimes.
Do you genuinely feel she would be better off having no relationship with her father? Not because of what you think of him, but because he’s her father. You need to be honest with yourself about that, and not allow your own views to cloud your judgement.
There are absolutely valid reasons why a child might choose to not see their father or to stay there, but there is middle ground between that and simply allowing the relationship to end.