Agree with both posters above. It seems like she wants to get back together with you, but as a married couple, not a girlfriend-boyfriend relationship anymore. I think this is up to you. If you are ready to take that commitment and all her 'childish' emotion, go for it. If you're not, that's ok too, let her go, and move on. Maybe you are not meant to be together, and that's nobody's fault.

Regarding her parents, I don't think this is the case of your break up. Her parents might be too strict, controlling, and/or abusive, but if they disapproved your relationship, it would be happened a long time ago maybe from the start.