It sounds to me that taking yourself out of the emotions that you are feeling and looking at it that way might help. To me it seems you should decide it is whatever you want it to be, regardless of what they think.
That being said, it is important that you tell them what your thoughts are so that they can adjust if need be. I would also do as they ask and stay out of their dynamic. At least enough to let them deal with each other. You can have whatever boundaries you like around the time you spend with them and how that is managed; whether it be no talking about their issues on certain date nights, and leaving a night to talk, or no talking at all about their stuff only, or whatever you want.
The point is to figure out your needs and then request them. This is the beginning of negotiating. Ask them to figure out theirs too and tell you what they are so that you can compare and move forward from there on what works and working on what doesn't. It's okay if there has been no discussion up until now. You just start now and work from there.
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