Have you been to the rental tribunal?

I am pretty sure that you can not be kicked out of a house if you have no where to go.

I am so sorry you are going through this. You are not a failure. You are doing everything you can for your little girl.

There should be some womens refuge centres that should put you up for a while and help you find a place. Do you have any friends you can move in with for a while? maybe instead of paying them rent you could make an arrangement that you will do all the cooking and cleaning around the house in exchange for a roof over your head whilst you save for a big up front payment of rent that might sway a landlord to take you on.

I really hope someone will pop in with some better advice than me. for you and your daughter.