I have been through this. 16 years living together, 3 children, though we were not married. So a weaker position legally than you - but I now have the house in my name, paying the mortgage myself. It sounds as if you are being very noble and moral about wanting yourself and your OH to split things equally, but if you haven't seen several solicitors (use the free half hour scheme to test them out), you are putting yourself and the children in a very vulnerable position. From what I learned from the process, it could go something like this:
Ask him to move out. Even just for 3 or 6 months initially. You need a breathing space and to check everything out legally and financially. Whether he stays with friends, bedsit or whatever is up to him. His name will stay on the mortgage initially and in an ideal world he would contribute to this. You may find he does to start with, then payments stop if he meets someone else/loses job etc, but it is a start. Until he has left, the sums are all a bit academic and the fours will be on what you and he can 'afford', i e. you are still thinking as a couple. This focus needs to shift to the needs of you and the children as a household going forward.
The day he leaves, claim tax credits. It sound like you have a similar gross income to me, though I worked full-time. If the number of hours you work qualify for the childcare element, and all the providers you use are Ofsted registered, you should recrive 70% of your childcare costs back. This is a game changer. You also get some basic tax credits per child, even to a fairly high income level, so with four DC, this should really add up. There is a tax credits calculator online and you can try this now, put the figures in as if you are single and paying for everything yourself. I don't think they count any child maintenance paid as income, but the calculator screen will tell you what to do. Once you actually claim and have a notice from them of your entitlement, your mortgage company should take this into account. Mine did, and it really helped offset that thing where they count the children against your earnings.
Get child maintenance organised. We had a voluntary arrangement to start with, ( trying to do things nicely), this started being reduced when he decided he wanted a nicer flat etc and stopped dead when he moved in with someone else. I then had to claim under the old CSA. This went onto a monthly direct debit scheme, collected by the CSA and counted as income for mortgage purposes as well. I think it is a bit more difficult now as the new scheme tries to encourage the voluntary route and that may not be counted as income by some banks. But a good independent mortgage broker could advise on that. Or if you can get the maintenance onto the next level in the scheme, (not suggesting your husband would default on voluntary, just that it is seen as more secure by banks), that may help. I would ring Child Maintenance Options for advice on this.
Get advice from several solicitors re. the house. This is free to start with so does not commit you to anything. I was told that had we been married, with my having main care of the three children, and it being a fairly modest house (three bed in nice area), and ex having slightly higher earnings and earnings potential, I would most likely have been awarded all of the equity in the house as part of a divorce settlement. So no need to find extra money to buy him out. As I was not married, he claimed half equity under property law, long story and eventually got sorted, but you are in a much stronger position. You could then need to take over the mortgage (from your new stronger position with tax credits and maintenance in place). Or if it is a very high value house or other complications that mean he retains some equity, the split can be decided by the court but the sale deferred until youngest child is 18, or completed HE, or older maybe if SEN. He might then remain on and contributing to the mortgage. Lots of reasonable options were outlined by the solicitors but not one suggested me and the children leaving the house if we had been married. If you are still thinking of moving out and leaving him in the house, if your name is still on the mortgage and he loses his job (alcohol dependecy/redundancy?), you are still liable for the whole monthly payments or can get your credit rating affected. And/if he later refuses to sell or has someone else move in, your could be stuck in rented and have to take expensive legal action to force a sale and get your equity out. I have a friend who moved out with her children and this has happened to her.
However much you want a friendly and cooperative outcome to this, celebrating Christmas together and so on....for the sake of your children and your/their future economic security it is time to get professional advice fast. It is much easier to get an amicable legal settlement early on rather than a few years down the line when other partners are involved (or maybe your hushand's alcohol dependency worsens).
With luck you could stay in your home and possibly keep an amicable relationship. The few people I know that have achieved that have had good professional advice and got things settled early.