As you pointed out, your boyfriend’s mother is very protective of her son. She may feel that he is too young to be this serious about a girlfriend. When you stay over at his house, you are putting your involvement with him right in her face. It’s too much for her to accept – especially in her home.
You are not going to change the relationship between your boyfriend and his mother. He isn’t ready to make the kind of separation that would be required for him to choose you over her. He is still dependent on her and he loves and respects her. That doesn’t mean that he doesn’t love you.
If you want to win her over, I suggest you take a step back. Don’t insist on being at his house. Date. Go out and do fun things together. Be respectful whenever you see his mother. Show yourself to be a mature and caring person who wants what she wants — what is best for her son. Ultimately, the approval of parents is what most ensures stability in a relationship so it’s important to do everything you can to improve your relationship with his mom.
Soon you will be at university where you both have more freedom to explore your relationship without being under the watchful eyes of your parents. It’s not too long to wait if you want to give your relationship a chance.
I wish you well.