Bank statements wont prove anything. I could change my address today and ask for a 12 month statement tomorrow, right?
I'd have a good look for an official letter with a date older than 12 months. Also if you or your mother claim any benefits that should confirm household occupants.
Just to note, you dont *need* to be a joint tenant to succeed a tenancy upon death. Seems like your asking them to create a joint tenancy so, should anything happen, you would still have to prove you lived there.