When you say "We", do you mean soon-to-be-ex husband (STBXH) did it with you and the DC?
The very first step, before booking a solicitor, before opening a spreadsheet, before thinking about the house, before any of the big decisions that will come in the next days and weeks and months, is to get your head round the relationship ending.
It is over.
You are now a single person.
Let me say that again:
You are now single.
Just because circumstances force you to live in a house with him, doesn't mean you act like a couple.
A. Search for all his financial information, just in case he tries to hide assets and cheat you out of a fair settlement. This is the first step because you have to do it before he realises what is happening and has a chance to hide stuff.
It may already be too late, if he has planned ahead.
B. Tell the children as soon as you have done step A.
C. Move him or you out of the shared bedroom. If he refuses, move all your clothes and toiletries and everything else out. Find space elsewhere. Sleep on the sofa or on a mattress in the DC room if you have to.
D. Stop all shared meals and shared food. Sort out the cupboards in the kitchen into 'his' and 'hers'. Label the shelves in the fridge, or just tell him which are his. There is no need to be petty - you can still share ketchup and salt, for convenience. Then you shop and cook only for you and the DC.
Ask him for a plan for which days he will shop and cook for the DC. He won't be able to give you a rota, but if/when he announces that he will cook tonight or tomorrow, you tell him you won't be eating with him and go out.
Never sit down to a shared meal with him.
He will tell you that you are being stupid, unreasonable, spiteful, crazy, etc. etc. You are not. Single people who share space with flatmates don't have joint shopping and joint meals.
He will waste money on takeaways when you don't cook for him, just to prove a point. Let him.
Don't talk to him about anything except practical day-to-day arrangements for the children. Nothing else. Just don't talk to him. Absolutely don't get into arguments with him.
E. Sort day-to-day finances. Don't get bogged down in the big picture or final settlement yet.
Contact the bank and get your name taken off any joint accounts. Take half of what is in any joint instant-access savings.
Leave the direct debits for bills to come out of the current account which is now in his name only. Arrange to pay halves on household bills, so you pay into the account that the direct debits come out of.
F. Stop doing any laundry for him.
G. Never clean or tidy the room where he sleeps.
It will be a hopeless task to get him to stick to a rota for cleaning communal area, so just clean them as much as you fancy, or not. Don't thank him or make any comment when/if he cleans a communal area.
H. Work on the assumption that you are 100% the parent, no 50/50 or set days for him to have them (not yet), so don't bother to ask him about when he is working or available. Don't ask him for anything.
Instead, if you want to go out you either do it on the spur of the moment when he is around, or you plan ahead and book a babysitter. Tell him when you book a babysitter. If he says there is no need, or objects, tell him that you cannot plan around his work schedule so you do need a babysitter and will book one.
Then, when you feel ready, contact a solicitor, start making decisions, and get the ball rolling.