I have challenged the CSA assessment all the way through the Agency standard method, through the complaints procedure (currently getting personal calls from the Senior Resolutions Manager), with my MP, and shortly to go to court.
You should do the same.
You should also phone the local JobCentre Plus and make an appointment to see the Lone Parent Advisor. They will be able to tell you if there is any money (tax credits, other top-ups, heating allowance etc etc) that you are entitled to.
As for not being controlled by him - you are being controlled. You're letting him call the shots, then letting him sit about your house drinking tea, then getting upset when he acts like a c*nt. Why is he sitting in your house insulting you? Because you let him in and offered him a drink. Don't let him sit down, and tell him why - it's because he doesn't show you respect in your own home.
Stop spending time with him, for a start. Teach him some new boundaries, which you control.
You say you can't just drop her off, or change the pick up time... Why? He can. Why can't you? Don't say, 'oh because', because then that's still you, letting him run things. This weekend, ring him half an hour before he arrives and say you're off out, he'll have to come later. When he flips, point out that the arrangements are never fixed - he's always changing.
All this being on your own is tough, and you have to get tough. Not least with yourself.
He isn't going to change himself, so you have to either change him, or change yourself. That's the only way to improve the relationship you now have with him. Which sounds, basically, as though the two of you are still reliving your break-up every day.
Sorry to be so blunt, but that's how it seems to me.
Do sort out the money thing, though.