I think you are saying that your boyfriend and his ex were still very much acting like they were a family unit. They had shared apartment keys and shared one vehicle. Once you moved in the ex started fighting with your boyfriend. You changed the visitation schedule with your daughters father in trying to make things better and have gone to counseling but you still feel ignored in this relationship.

Your 1st warning was that they were still sharing not only house keys but a car. That relationship wasn't over yet. Even if they were seperated. They are still far too enmeshed. The right thing to do is move back out with your daughter and find someone who is actually single. Look at this as a hard life lesson for both you and your daughter. Be very careful next time about moving in with a man with a child- the same should be said for someone moving in with you. You are a mother and you 1st priority should be your daughters health and wellbeing. Moving in and out with men is not going to be the right thing for her so next time make sure that it is going to last. We are all allowed to make mistakes- lord knows I have!! However, this is where you learn and make sure not to repeat those mistakes. 

I wish you and your daughter the best and I hope you find a good partner in life that is ready to have you and make a life with you!!

*****My take on what was written, leaving it mostly as was. Hoping the OP doesn't take offense to my doing so. *****

"I have got to the end,  I think, of our relationship, as I have had enough. 

I left my house, my life, everything to move onto my partner's house.  He has a son that he was seeing every weekend. Me and my daughter moved in with him.  His son and my daughter were the same age.

 At the time he had keys to his ex's flat and she to his.  She didn't like the fact she had to give him the keys back.  They also were sharing a car. After a while it was getting on my nerves.  We also had to ask her permission to be able to go out at the weekend to see if she would have her own son.

Anyway, we started rowing a lot.  My daughter goes to her dad's every other weekend.  So then he (my partner) changed it (partner's parenting time) to every other weekend.  Since he has done that, when he has his son we don't have any family days.

It's as if he is obsessed with his son. He goes off with his son.  My daughter and I get ignored until his son goes on a Monday.  When we all walk up to the school together, he completely ignores us. My daughter and I have had enough. Now we can never be a family unit.

I have had to put up with so much from his ex that he says is my problem.  We went to counseling for 20 but things have gotten worse"

You are a consenting couple sharing a bed and space. It takes a few years for a blended 'family'. It doesn't just happen because you move in.  This is a huge misconception. 

This man is not ready for a move in partner. He is ready for someone to have sex with and hang out with at his convenience. Anyone here will point out moving in when his ex still had access to his home and he has access to hers is a HUGE red flag.. He has given her key back, right? My DH tried the same crap "I need a key in case the kids forget something.: So they wait until their mother is home  and THEN go over."But it might be an emergency..." I think this was a video game type emergency (eyeroll). I told him to not even ASK her unless he wants her to have access to our place and I would never let her have a key and I suspect she wouldn't want one.

Move out so he can be the parent he wants to be. Make some boundaries for him as well. Right now you are complaining about a situation that was obvious from the beginning. Just remember having sex with someone does not mean you have to move in. And show your daughter it is perfectly OK to live on your own and be your own person.

as a bed warmer and nothing more - he has made that obvious.

Time to leave and obtain your freedome!