You need to sort out your finances first.
How much equity is in the house and can either one of you buy the other out, or will it have to be sold?
How much in savings, investments and pensions is there?
If you don't have a job/parttime then that needs to change.
Go on the benefits calculator and see what help you might get, especially with rent and childcare costs.
In the meantime start living separately in the same house. Separate beds, separate laundry, separate shopping and cooking. Split the childcare into 50/50 and let him be a sole parent during "his" time, ie feeding them, shopping, pickups from school, breakfast run, sorting out care, washing etc. Don't give in on this as it will make your 50/50 and cms claim easier once you are properly apart. It will bring the reality of parenting to him and whether he can actually adapt his life enough.
Remember - you can break up for any or no reason at all. But you do need to think the finances through properly which will involve losing the marital home. Downsizing or rental or in a totally different location or all three is the norm. Get on rigtmove to look at your options. Plan, plan and plan again, then execute that plan. It can be done 