Sounds like a bit of a rough start and that each man is trying to man up the other. *yawn*
That gets totally old for me pretty quick.
If I were you I would first of all be expressing my need for all of you to get together and talk it all out face to face. It doesn't have to be now, but at some point. If I were you I would be letting them both know that this is not an option for you. Its expected at the start of a poly relationship. You might not get your expectation filled right away, but when they see that it really is important.... Sorry, I'm a stickler for that one. Its just not good poly ethics to me under your circumstances to not have metamours meet.
Often the competitive stuff stops when someone is right in front of you. The two of them can work on their relationship in terms of setting some boundaries about your time with each of them, what each other says in terms of what is passed on and checking their words before saying them.
The other thing is that YOU get to say who you sleep with on that week. Its not their choice. You are not a pawn. The only thing they get to do us to let you know if you are not spending enough time with them and they feel left out, so that you can discuss with the other and adjust your time schedule. Really, to me a large part of how poly works is to be considerate of each other. Especially metamours.
I am wondering how much reading you have done beyond your thread. A lot of all this has been written on and could be useful. I suggest doing a search in the tags for "metamour" and anything else that you think could be relevant. Maybe it would help. "poly lessons learned" is a good thread in the stickies that might help also.