Should I keep texting her?

I think you'd better give up. Listen to you, his parents don't support you, and you have broken up. So if you want to make up with her now, there is a lot of resistance, even your girlfriend is willing to get back together with you, but her parents' attitude also determines that it is difficult for you to be together in the future. Besides, from what you described, I feel that your girlfriend doesn't really want to be with you, so break up with her before it gets too stiff and leave a good impression on her.