I hope you have run various scenarios through a benefit checker?
If the house is HA - Talk to them, they could try to find you another. Or even move H to a flat, making you the tenant of the house. It may be a long shot but you never hit anything if you don't shoot!
If it's Services accommodation - Policy is to move him into single accommodation while you stay in the house with the kids. He has to pay both rents for 3 months.
If it's tied accommodation - Messy. If you know there's an unoccupied property, it would be worth finding out if you could take it for a transitional period. They'd discuss it with H though, so you'd have to be on the same page. Big corporations will have a formal policy on marriage breakdown.
If owned by his family - Also likely to be messy, but don't assume anything. They may have strong views on infidelity, for instance, or on keeping children in a stable situation. Shoot the shot!
Don't do any of the above before lining up your ducks, securing paperwork and money, etc. But do explore the possibilities.
Good to hear you're going to talk to your parents, too. Wishing you a following wind.