You need to respect everyone with whom you are involved, not just one of them. Your girlfriend's emotions and how she handles them are not your responsibility. It is possible that becoming crippled by her own feelings is a strategy she employs to control situations that make her uncomfortable. In other words, a manipulation- though it may be a completely unconscious reaction.
Tossing away another relationship in deference to her meltdowns would likely do nothing to help her deal with the root cause of her emotional storms, and it would be callous to the other person with whom you are involved - you would be sending a message that they are unimportant compared to her.
I would fathom a guess that a fear of losing control and deep insecurity is at the core of her problem - and those definitely require inner work, not you placating her. She may benefit from intensive therapy, counseling, or possibly medication if her emotions are that crippling to her.