Calm down a little everyone?
Whether you agree with the op it not, she's frightened of what's happening around her and confused about everything.
Denial? Perhaps, but her whole life is crashing around her ears and she wants none of this to be happening.
Social services would indeed look up and take notice of this situation but seriously, swoop in and take your child? Don't be daft. There are kids being thrown against walls and starved to death and they don't get taken. To say they will take this dd is scaremongering.
Actually the op would benefit from getting advice from SS, but all this frothing will drive her away from this.
Op, take a breath. It will be ok. It will be ok because you know deep down what you have to do.
You have the means to do it too, so it's only fear of taking that's two and what it will say about your family that is preventing you.
This is not your shame. This is not something you caused. You can't even change what's happening here, only your reaction.
It is imperative that you get yourself and dd into a more healthy environment. You talked about leaving a couple of months ago, but didn't. The right thing would have been for you to have stuck with that plan, but I know you hoped things would change, and you clung to the sign of hope you saw.
Ok so veil is lifted and you know now that it's a dead end street. So dig deep and do what you gotta do.
Go check into a bandb for a week, go back to your plan and buy some headspace.
The priority is to defuse the toxic envieonment you're in. Once you're out you can take steps to work out what needs to happen next.
You can get out tomorrow, tonight even. Even if it's a hotel tonight, and look for a B and B tomorrow, you can do this.
Don't rule out any authorities for help, that's what they are there for and they will want to make sure you have everything you need to manage the situation yourself. The last thing they want to do is take your child and have to find money to look after her etc. As long as you're makin the right decisions for her, they will be behind you all the way.
You can do this.