Hi Torn and welcome to the forums. I really am not sure what to say. I think you said it best. It sounds like a crazy arrangement and maybe not the best one to suit your needs and wants in a relationship. I have to be honest and say that I think you should end the relationship and find someone more suitable for you. Someone who loves and respects you. He may love you in some way but he is not respecting either you or this other woman. It's not fair to either of you. You deserve to have a relationship with a man who will love you completely and devote his life to you and your life together.
I wish you the best in trying to figure this out.
Heidu