If you are going to be the main carer, you should get more than 50% of the house equity. I got over 60% which is admittedly a good deal, a friend got 60%.
Would it be possible to sell the house, use your equity as a deposit and buy something new? I know it's expensive - same where I live - but I found a relatively cheap modern flat. Look at flat floor layouts carefully, sometimes you can carve 3 bedrooms out of a 1 bed or 2 bed, for example if it has a boxroom and a larger kitchen which can be made into a live-in kitchen, then the living room can become a bedroom. Or sometimes if a living room has 2 windows you could divide it into 2 smaller bedrooms and use a smaller room as a living space. I have a box room myself but it's worth it to be single.
I agree the maintenance you are entitled to is not much compared to his salary - my ex earns similar and my solicitor was shocked that he chose to pay only the minimum. (He still pleads poverty though on his 3K+ a month take-home 
) However because I did get a good split of the capital, I'm in an ok position.
The deal my solicitor thrashed out also included him paying half the childcare costs on top of that though - after all they are his kids too and childcare allows us both to work, not just you. Having said that, these costs are much lower as kids are in school.
Get yourself a good solicitor and get either a free initial consultation or pay if you possibly can, for an hour with the best you can find (look at reviews online, my solicitor also came up in news stories where she had kicked ass in the family courts).
Make sure you tell the solicitor everything including about the drink problem. Try to get evidence of his salary in print, for example if you can get hold of his P60, or statements from a bank account showing his salary going in.
A childminder might turn out to be a better childcare option. And I would NOT give up work, you are going to need your career.
If this is all too much at the moment, and I understand if it is, your other option is to bide your time, disengage from him completely emotionally, start building your own savings, keep detailed notes about his behaviour (well hidden of course) and plan your exit slowly and carefully. This in itself will make you feel less trapped and more in control. If you can wait until you have at least one child in school, or maybe in a school nursery with wraparound childminder, it will become cheaper.
Lastly I used to imagine myself looking back from the future and telling myself I did it, I got out. It gave me hope, and now I'm here. You can do it and you can have a happier future.