Yes, please get rid of the arbitrary rules, that only serve to put your girlfriend in an extremely awkward, and almost certainly unwanted, situation. It's good to have rules and boundaries, but maybe think of why you have them before you set them up?
For example, the no cum rule? What the hell for? And the no sex with just her and you, and her and him, makes it sound like you are (in fact you rather admitted as much) insecure with YOUR and HIS relationship.
And, if that is truly the case, then it isn't fair to lead your girlfriend on with the idea that you will truly care for her, and be happy for her relationship with him. She'll only end up getting pushed out, or feel like she's pushed you out, if it comes to that. Don't do that, please.