Okasy I think that your b/f has no back bone. It sounds like when things get tough he gives in. Who is the parent? He also needs to tell his mom to back off. He did not tell her how to be a parent to him. My mom has been great in that respect. The rules that are set in my house are also in her house. It sounds like the 14 year old thinks that when things get tough she can run to grandma. She needs a hard dose of reality that grandma is not always going to be there. It also sounds like she knows how to push the buttons and has been doing so for a long time. Old habbits are hard to break but now is a good time to break them. It also tells you something is going on when the mother sides with her b/f rather than face off with her child. To me it sounds like she has been pushed to the side and forgotten about and this is her way for getting the attention she seeks.
Maybe taking her shopping or out to lunch for some one on one time. Maybe that will help her to open up to you and her to respect you.
The other thing that I think you should do is seek a therapist or someone who can help address these issues. The birth mother needs to be included in on this especially since it sounds like she is shutting her out.
It might be stressful for you but it also sounds like this is her way of getting the attention that she was not getting from her parents. Grandma giving really is not helping the situation so maybe you and your b/f need to talk about your apporach to grandma.
Hope this helps, maybe gives you some ideas.