Also, you keep calling him "the child"--
Well, I think "the child" would be better off without you in the picture because you have not accepted him.
I'm sorry, but if your bf has 50 percent custody--he is doing a decent job.
If you don't like how the relationship is right now--it will not get better down the road (marriage). You should probably date someone without children.
It sounds like you have a very difficult situation. You mentioned the son has been living with your boyfriends parents and always has - this in its self can have a large impact on the childs behaviour. Imagine being passed on from one care giver to another, each having different ways of parenting and handling situations. The son is most likely getting so many different mixed messages. One cannot expect a child of such a young age to be a perfect well behaved child. Behaviour is learned, esp by example esp from loved ones and role models. I feel deeply sorry for this child as it seems he probably has no stability in his life.
You mention that you make excuses for his son not to stay over. You must be terribly angry and frustrated but in reality you are denying your boyfriend and his son a chance to bond and form a deeper relationship. I think this is what the son needs. Perhaps his behaviour would improve in time. Perhaps he needs to be loved and appreciated. Being a parent is not easy. It's a huge responsibility. Being a step parent is even more difficult. You would have to first accept the child, be able to love him regardless of his unacceptable behaviour.
It sounds like your boyfriend has lost respect for you (he probably resents the fact that you dont accept his son yet) and you have lost respect for him too as you are not his no.1. If you aren't truly committed to both relationships then I suggest you end the relationship as any negativity and resentment towards each other will fall onto the child and affect his behaviour even more.
Good luck.
Do the boy a favor and get out of the relationship with his Dad. Yes, he should expect his son to respect you but you really sound as if you do not respect him. It's sounds as if you can not stand this child and therefore I feel sorry for you. If you do not accept his son, you might as well move on.
You sound like you have no experience with kids. Tha'ts what they do! They go in and out - they want to be entertained, they get bored, they jump on things. This is not ADD. It's called being a kid. You were once one believe it or not! Maybe you still are because you sound very young - you need to get out of this relationship and grow up.