Fedup you are doing a huge amount of compromising right now. When you talk of compromising, I think you're talking about the flat, your living quarters.
But you're not seeing the devastation that this relationship, this emotional environment, is having on you.
WRT the 'equal relationship' -- this is very far from being an equal relationship. Equality has nothing to do with money. It's about mutual respect. Does he insist that you ask him to go to the library or to go swimming? Does he ask you for permission to go out when he wants to? I think the answer is probably no, as he unilaterally decided not to go to the park with the DD without talking about whether this would inconvenience you.
Advertise in Gumtree and even put up a notice in the DD's nursery if you can. It's not weird. But I think you should go to Women's Aid and get help from them.
He may well have the flat, but you have rights to the flat too and to live there, and he cannot use the flat to end the relationship.
And really, it IS domestic abuse. PLEASE, PLEASE go to Women's Aid. You will be no use to your DD if he succeeds in injuring you, putting yo in the hospital.
He has nothing to lose true, except his wife and DD? PLEASE stop looking at this situation from the pov of losing the flat. PLEASE.
If he cared about you at all he would treat you well, and would not be running after you with his fists clenched threatening to hit you. This relationship is not worth caring about. You are getting nothing out of it that is truly good for you and neither is your DD.
(BTW, he is a crap father. A really crap father. There is nothing in your posts to suggest he has any redeeming qualities in this area. Your DD will be terrified of him as she grows up if she isn't already.)
Read the book "Why Does He Do That? Inside the Minds of Angry and Controlling Men" by Lundy Bancroft. You will see your H in the pages; not a pretty sight, and you will see that he is the one who has no hope of having a good relationship, with anyone. There is no cure for what he has, and it is poison to any relationship.
You on the other hand, can go on and possibly enjoy a lovely and fulfilling relationship with some nice, decent someone, the kind of good, healthy relationship you deserve.