From what you have said OP his family have probably ensured, because they aren't married, and he has been paying what, the mortgage, bills, put most of the house deposit in, she hasn't seen any paperwork, did she sign for the mortgage, when the annual mortgage statement comes through is it addressed to both of them? Sounds like it isn't if you are asking these questions on her behalf.
So I am guessing, no she isn't entitled to anything regarding the house. But if he is insistent that it is going to the kids anyway, then that is a small comfort. Although if they split, he meets and marries someone in the future, they might have kids there is a chance their kids are left with nothing.
It sounds like she has been extremely financially naive and is going to have to walk out of there, get a better job, get child maintenance and split childcare so she can work.
As for the council, that will be area dependent. She would probably get temporary housing, that might be temporary for a long time, or might be lucky and get housed straight away. She can only try.