You have gotten a lot of great advice and most of this has already been said, but you have set the boundaries. I have BF kid issues, too, although a bit different than yours. When his kiddo is around, the kiddo knows that he is to do what I ask him to do and if he is disrespectful or shouts at me, I can deal with it or get his dad to. The one time he shouted at me that I am not his mom, I asked him to please not shoot me with his Nerf cross bow gun thing. I took the toy and he scrubbed the baseboards with a tooth brush for ten minutes to earn it back. Afterwards, I sat down and explained that while I am not his mother, he is in my house and I love his dad very much, so that kinda makes us a little family. People in families respect each other, even if they don't like what is being said or done. I explained that is a non-negotiable expectation, and if the behavior happens again, then he, his dad, and myself would sit down and discuss further this concept. There have been no other problems.

Dad wasn't too happy about the punishment aspect, but I gently reminded him that this is a new situation for all of us. I reacted the way I would with a kid in my classroom and I didn't want to depend on him for all of the respect the child shows me. I needed to set boundaries on my own. I would never yell, hit, or be hurtful toward the kid. After the initial shock of the situation, he was cool with it and backed me up.

Have you talked to the dad about your problems and let him that if you are going to be together you are going to be a bigger part of their lives and boundaries need to be established?