Huge non MN hugs. I've been where you are, but I asked my exH to leave temporarily.
My DC were 13 months and 4.
You sound awesome, strong and calm, (although you don't feel it).
Be simply truthful to DC, "daddy is staying at cousin" short and truthful.
See yourself as a single parent (even if temporarily), you are the boss now in your home. Friday after school, do something nice, even just a walk in the park.
My advice is, if you know anyone at school who is divorced, discreetly ask which solicitors they used - there are some brilliant and some awful solicitors out there.
Call Jobcentre+, make an application for benefits - and set payment up into your personal account. Call tax credits and make a single person application. Once you have both these in place you'll be able to apply for council tax benefit, free school meals and pupil premium.
When you see the solicitors don't take legal aid - the costs are accrued against your property.
Get copies of your husband p60/national insurance number. Make sure you have access to your bank accounts, passports, which solicitors hold your deeds, and your marriage certificate.
Stay strong, stay calm, hold your DC tight. And be kind to yourself. Things will get worse before they get better.
I'm 7 years post split, my life is good. My DC are happy, smart, funny and kind in spite of everything.