It makes it harder that you're related to the girl's dad, I think. If you don't normally/often see her, you can't easily approach her and say "So, do you actually want to see your dad?", and if you say 'no' to her mum's request, then you're probably going to get some flak.
I think you're in a v difficult position. Tbh, I think your best bet is to talk to the girl's mum, and say you are worried that it will make it worse for the girl if her dad wanders into her life at this point - that you think he might not be very supportive and realise that that would be very bad for her.
FWIW, my own DS (17) has seen hardly anything of his dad throughout his life, and nothing at all of him for about 4 years. It has certainly caused him some problems and a lot of distress. But to be honest, the worst times have been when his dad has made contact or got his hopes up and then not stuck to promises.
When my DS1 was very tiny, and my relationship with his dad was breaking down, his sister said something to me that was critical of him and very helpful to me, because it made me realise that even his family recognised he wasn't going to stick around and be a good dad. Maybe her mum needs to hear something like this from you...?