From what you are describing, it sounds to me like both of these people aren't very good friends to you and haven't been for some time. I know that when you start a relationship, it's all very exciting and the siren call to spend all of your spare time with the other person is very hard to resist. But, ditching your other friends to isolate yourself with one person isn't healthy and probably doesn't bode well for a long term relationship. And consistently lying to you and acting in ways that could be interpreted as them letting you know that you don't mean as much to them as they do to each other (cancelling plans and then hanging out as scheduled without you being there) don't seem like the characteristics of true friends. It is tricky to believe this though, and even trickier to let it (them) go in favor of more positive, healthier relationships.

There is something positive to be taken from your recognizing that this is a vicious cycle and you want it to stop.

I wish I knew the answers to how to break the cycle. Maybe it would help to come up with a list of distractions that you can turn to whenever the urge to lash out at either them or you comes on? I've been trying exercise to help me with a somewhat similar situation - figure if I go for a 15-30 minute walk every time I feel the emotions connected to a particular relationship start to overwhelm me, I'll hopefully not only distract myself long enough to make a better decision, I'll help address some of my weight issues.

Sending you lots of thoughts of support!