Hi Belle,

Sad to see you asking that question. Hope you'll find a way to settle everything in the best way.

The information given by Mark is correct.
You have ILR...Indefinite Leave to Remain. You currently have virtually the same rights as a British Citizen except that you cannot leave UK for 2 years or more. If you do you'll lose that ILR.
Also until you become British Citizen you're not eligible for a British Passport.

Your visa cannot be cancelled.
You can legally claim whatever benefits/public funds you are entitled to without any concern.
No-one here can give any legal confirmation on the questions relating to the children.....that's a question to be settled between you and your husband and in cases of disagreement also the courts.

Hope everything turns out well.