When I said that she doesn't seem mature enough, I meant in age and experience. I knew that dating a guy with two teenage girls would not have worked for a twenty-something me. I would have found it to be a huge imposition on my life. In my thirties, I could have possibly opened up to the possibilities, but not until then. If we're talking biases, this would be mine.
Is the family a drama bomb? Maybe, but she sounds defensive enough that the story seems painted so that she comes out on top no matter what. My guess here (just a hunch) is that that her boyfriend has sensed that the OP is probably too young and busy to enmesh herself in his life and is acting out of fear. I'll agree he's not handling it great. Confronting her at her workplace was inappropriate.
Either way, as mentioned, the issue seems to be incompatibility due to no real fault of hers. Wrong time, wrong guy.
“Inside every cynical person, there is a disappointed idealist”--George Carlin