You will have rights but your name not being on the house could lead to complications if you do split. In the words of a very wise solicitor, nobody ever knows what is around the corner so protect yourself financially.
I’m not saying he will, but if he did choose to leave, you would be in a very vulnerable position. If something happened to him, it could be very difficult for you to access money.
Financial control/ abuse- whatever you want to call it starts slowly usually. As someone who has experienced it, you don’t necessarily realise what’s happening. There are a lot of red flags in your posts and I would be concerned if I was you.
Him not supporting you through maternity leave is exactly what I experienced amongst many other things. However, we did not have a joint account and I insisted my name be on the house.
As some have pointed out, the first port of call should be to have a discussion with him. However, if that was an easy task, I think you would have done that rather than posted on here. My ex husband used to flare up any time money was mentioned in order to put me off mentioning it. It worked.
If you can’t talk to him. I hope that you seek advice and begin to put your ducks in a row.