The domicile requirement is for the I-864 affidavit of support. I looked at the Foreign Affairs Manual that gives you the "legal" ruling of what the visa officer uses as a guideline. I have been living in my foreign spouse's country for the past decade. In my opinion, your best resource will be people in your similar situation interviewing at the same consulate. I prepared a bunch of documents because I assumed my consulate would be that strict but luckily they were satisfied with what I provided. Since you have no proof of current domicile, you will need to focus on establishing a strong case for Intent to reestablish domicile. You have young kids and school enrollment is a strong indicator. But most schools require proof of domicile within their district. 😬
Good luck! And hopefully someone with your similar situation that interviewed in the consulate you designated for the visa interview reaches out....you could also look at the UK consulate reviews here on visa journey and find a member who seems approachable and send them a private message?