Your 13-year old stepdaughter hates you. Admits she hates you. Admits she thinks her mother can do better than you, and in any event wants her mother to get back with her father.
Sucks to be you, I know.
Here's how you can make things worse: Sleep with her.
Doesn't matter if you say she "started" it. Doesn't matter if you say it was only six times, not the 75 she says. Doesn't matter if you say she flirted and dressed suggestively. Doesn't matter if you say you did it with her initially because you were scared of her and then later fell in love with her.
Once you say "Yes, we did it," you're done. Over. In prison. For 16 years.
Nothing else matters.