I vote for you standing up for yourself and not allowing yourself to be used.
Sounds like there's a lot of potential there for you to get hurt.
One of the common wisdoms around here is that this doesn't work:
Relationship broken, add more people.
If you guys have a shot at being open, it appears that you may have to just be two for awhile.
It also sounds like maybe you both need to work on yourselves for a bit; and get MUCH much better at communication. If she's going to sign off in anger when you want a conversation, that doesn't bode well for communication in general.
Wishing you much luck.
Love is that condition in which the happiness of another person is essential to your own...
Robert A. Heinlein
Me: female, bi, (formerly hinge of a vee)
with FirstBoyFriend (FBF)(moderately long-distance)
and no longer with CurrentBoyFriend (CBF)(who lives in the apartment building next door)