Someone else mentioned this and I don't know if it will be read but I feel compelled to say it.
The daughter is of the age she's probably perfectly aware of what's going on. If she doesn't she will after her mom asks her to lock her door. Girls gossip.
You don't only have to worry about your partners apparent willingness to jump the gun to assuming you're going to abuse her child even after all this time. But you have to also worry about the daughter piecing her mother's irrational worry together and gossiping with a friend at the wrong place at the wrong time. If she says something to a friend like "oh yeah my mom doesn't trust him not to touch me" and that soreads, perhaps the friend says something to their mom (whatever) shits going to get bad for you really quickly. Nothing will erase the stigma attached to you your partner is creating if it gets out out or context.
I don't think I need to mention someone that willing to believe that from you is probably likely to say something out of anger along those lines that will also cause you problems beyond a simple insult that cuts you to the bone.
I don't think any of this is you but she seems inherently unable to trust any man when it comes to family. And you aren't going to magically change this. If you choose to ride it out you have to be aware that the environment of distrust she's breeding could backfire on you terribly. I'm also sorry to say while I don't know the kid, she wouldn't be the first in an act of rebellion to say something out of anger that her mom could misinterpret either.
Basically nothing about this relationship described is a good headway into any resemblance of a normal family dynamic for you. If that's what you ultimately want with a partner or even just to protect yourself from paranoia in the future... Take a moment to think to yourself if this is the right place to be in. She could benefit from therapy on a personal level but it takes a long time to start to errode fear like that.
I don't know. I'm rambling. Protect your head, heart, and reputation OP.