It might be best to reframe this. No one can say for sure whether or not it's right for you to give them a second chance. Clearly, you think you should and if you were single that would be the end of the discussion because in the end it's a subjective question. We can't really know whether they've changed their ways, maybe they have.
But your actions affect more than you, so I think the REAL question is -- is it right for you to get involved with them even though your gf has valid concerns about them? I think that, if you really care about her, the answer is no, it's not right. It would be one thing if her concerns about them were baseless and she was just being paranoid, but that's just not the case. It's very, very reasonable to not want your bf to be involved with a cheater and with someone who's disrespected and frightened you.
So, instead of asking yourself if they deserve a second chance, ask yourself if your gf deserves someone who's willing to respect her legitimate feelings.
The major players. Me, under-30 bi female. Gia, girlfriend of 3+ years. Clay, new boyfriend/dom. Davis, ex/"it's complicated."
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy, Clay's partner.