To be clear:
He 'views' the house as his (but you are married and it is jointly yours).
He works in paid employment (so believes he is 'worth more' than you).
You look after young children and get no 'payment' (i.e. not even the tax credits). You also get no 'time off'.
He won't leave and you can't afford to leave.
He has never even watched a DVD with the kids, let alone anything more! (I am gobsmacked at this, even shit dads can watch TV with their offspring, I mean, seriously?!)
Please see another solicitor, steel yourself to be the one who 'makes it difficult' (although, of course, it's him that's doing that) and GET WHAT YOU ARE ENTITLED TO!
Which, for the avoidance of doubt is:
Money from the sale of the marital assets (house) and anything else you may be entitled to as an equal partner in the marriage.
Proper contact arrangements, so your children can build a relationship with their father and you get 'time off' to build your own new life.
A place to live that is your home, all yours.
Maintenance payments from your H's salary towards the upkeep of his children.
Get angry, OP. Don't try to be civil 'for the sake of the kids'. Does he do anything for them? Do they deserve to see his behaviour in a good light? Get angry and get some action started on evicting him from your life.
(BTW I don't mean scream and shout at him in front of them, I mean harness the anger and put it to postitive use by taking steps to get him out.)
Life may be miserable for a bit, but it will be miserable for a whole lot longer unless you get it sorted. Short-term pain, long-term gain. You have a responsibility to your DCs to be happy and the best mum you can be (especially if their father is rubbish), and you won't be that unless you steel yourself for some unpleasantness in the immediate future.