I love her, but my family are what's stopping her

Me and my ex have been split up for about 6 months, but I'm still hugely,head over heels in love with her. We went out for a year and a half, she ended it with me because of the relationship I have with my parents, I told them things I shouldnt have, but both me and my parents have learnt from that and grown from it. I've tried telling my ex that, but she doesn't believe me, she has said to me if I didn't live with them, it would be different, and she really doesn't seem 100% convinced on it even now. But there's another complication. There's another guy who she also likes, who she hasn't been with yet. When we were together we fought about him a lot! She has said she doesn't want to repeat the past. But I know she still has strong feelings for me. I met up with her recently and I can tell! Even though im only 17, this feelings so real to me, my life just hasn't been the same without her. How can I make her see that my family situation has changed, and make it so that we are both happy again.

You are 17 of course you are going to have a relationship with your parents, and where does she expect you to live at your age? She sounds immature and she is playing with your feelings, when someone cares about someone there is no one else, find your self a person who has only eyes for you, she is playing both you and this other guy, and using the excuse of what ever it is you told your parent, there are so many more worthy people out there who would not use that as a reason to break your heart, let her go and her ego. Sorry been there done that, do not waste your time and emotions on this, what she is doing is nasty.