I can see your are upset and take isn't a very nice experience, and quite possibly he isn't very nice in the way he goes about things.
However, he is her father and he wants 50% access - that does not automatically make him the bad guy. Lots of men want nothing to do with their children - at least he is still keen to be in her life.
It's not unreasonable that, as currently he only has EOW, he wants half of the school holidays - really that is positive - he wants to spend time with his kid.
The house I am afraid probably does have to be sold if you own it jointly - but as you paid the deposit a solicitor may be able to help you get a fair share of it back. Who currently pays the mortgage?
The car I wouldn't worry about as your dad owns that.
I think you just need to go to court and work out a way forward that is best for your daughter. Maybe the court will decide 59/59, but a solicitor can advise you on that. Can your parents help you pay for one if you can't afford it on your own?
You talk of him "threatening" mediation. But why are you scared of mediation - surely it would be a good thing?
Good luck. I know it is very hard, and difficult sometimes to see the wood fork the trees in these situatione.