No, don't give up. I was in a similar situation. I went to police but I didn't say no properly so nothing happened.
I think you should go to the police now, and then get into a refuge, it will be quick.
Report the rape, and they will do a video interview. It won't be nice but it will ensure he is interviewed over it, possibly arrested.
Go via a local domestic violence charity and ask for help in a refuge.
Once you're there you can have a support worker who will assist you applying for benefits.
You can give your ex contact with the child and use that time to sort things out. You can begin from scratch and when you do you feel better about yourself slowly but surely.
As long as you're giving him access you won't have to go to court.
If he begins not passing the child back you can go via your support worker to file a C100 and use legal aid to file it and gain a solicitor who will then help you through your divorce and any possible child arrangements proceedings .
You can't withhold the child, unless you have significant cause to believe he will put her in immediate danger, and if that's the case, deny access, but he will get 50/50 unless the above is the case via court.
I have felt and said exactly the same as you over these past few years, I submitted to sexual abuse, being called names, choked out, licked, dominated. It's soul destroying, and the nightly flashbacks are exhausting.
Please also go to your GP and get all these incidents and their effect on you, on record. Also you could get some short-term sleeping pills if you are having trouble once you get into your new home. I did! My sleeping pattern went absolutely haywire, and I had to juggle being with my child, processing abuse, working, and bouts of absolutely unmanageable anguished screaming.
It's almost a year on and even though he has maintained a level of control and terror over me via access to my child, I am able to live as myself, and find myself outside of that dominating relationship. I have been nothing but a mother for 7 years, and for 5 a submissive sex slave with limited and ever-decreasing freedom and autonomy.
Even though I am living my nightmare, which was having to hand my child over to someone who I know to be unstable and sexually perverse, I still feel freer than I've ever felt.
He wanted me to think I was better off killing myself and leaving my child to him. Don't do it! Don't let him take your life in that way.
Your children need you.
If you call Women's Aid tomorrow or a local domestic abuse place, or both, it may help you have the courage to report his crimes, and then you will have the ball rolling and life will be better.
You only feel this way now because he still has you under his physical control. You can end that though. Once you escape the physical control, you work on the mental control, but you can't do that until you're physically free.