Yes, there’s something seriously wrong with this woman. She doesn’t seem to want her “baby” to grow up and she is being competitive with you. But — your problem isn’t really with her. It’s with your boyfriend.
If your guy can’t begin to draw boundaries with his mother, I don’t see that the two of you can have a healthy adult relationship. He, not you, needs to tell her to stop using baby talk, to respect his time and his relationship and to stay out of his room. You can’t do that. He has to. Further, he has to do that in a mature way. That means being clear, calm and adult while insisting on a shift in their relationship. Until he does, he isn’t grown up enough for you to consider a future with him.
I suggest you stay away from his house until he does what he has to do to make a change. See each other at your house or on dates. There’s no need to put yourself in this situation.
I wish you well.