So sorry that you're having to deal with this, dodo 
It's no wonder you're so sad though, as he's got everything on his terms, and you are left to deal with everything - all the stress, all the domestic work and all the parenting.
You need to realise that you hold the cards here, really.
HE has decided to move out, so YOU decide when he can visit. Swanning in when he feels like it to assuage his guilt at dumping his wife and children is not an option you can allow him to carry on taking.
HE. IS. TAKING. THE. PISS.
I suggest you formalise the situation and suggest his time with his children is spent away from YOUR home.
Of course he should see his children regularly, but there is no reason that this should happen to your detriment. When do you get a break?
If he won't entertain the idea of counselling (and if he is holding the threat of finances over your head) then perhaps it is time to make a decision re the future of your relationship?
You cannot continue to allow him to take the fun bits and dump the crap on you.
Perhaps he is depressed, but you cannot force him to seek help, and he cannot be permitted to drag his family down with him.
There is nothing to say that a reconcilliation can't occur at a later date, but he needs to sort himself out, and you need to prtoect yourself and your children in the meantime.