Some background, DP and I have been together for almost 9yrs, since I was 15 and he was 17. When we were 18 and 20 he decided he wanted to buy a house, I fully supported him and agreed that as we were so young it would be silly for me to go on the mortgage as who knows what could happen 6 months down the line. Time has gone on and we are now 24 and 26, with a 4yo DD and we're getting married in a week and I want to go on the deeds.
DP doesn't agree. He says that he wants DD to have our house if he died (as of yet, he has no will). But with a clause to say that I can live here as long as I want to and that she won't be able to kick me out. He says this is because if I got a new partner, he wouldn't want this imaginary new partner to take the house away from me and DD and leave us with nothing 
I can kind of understand why he is so wary, his brother has been screwed over several times by past girlfriends and his whole family are of the 'take care of number one and sod anyone else' attitude so as well as what happened to his brother, it's the way he's been brought up. His mum even wanted me to sign some kind of contract to say I wouldn't screw him over before we moved in together, I don't know what it was and she never produced this document. I'm surprised she hasn't insisted on a pre-nup tbh.
All the bills are in his name, but I pay the council tax every month and the waste water every 6 months. I've put almost as much sweat and blood into this house as he has and I think it's high time the house was legally half mine.
What should I do?