My ex wants to get back together but her parents don’t want us to. What should we do

Me ‘15M’ and my ex ‘16F’ dated for a year and 7 months we broke up after a rumor of me cheating started circulating around my school. I pleaded that it wasn’t true but she didn’t believe me so she broke up with me.

For the whole summer I begged and told her it wasn’t true and I loved her so much, but she still didn’t believe it and it lead to more drama because we were crying and arguing and her parents found out about it and I don’t think that it really sat well with them. This kept going on until i finally gave up. We went into no contact for about a month until school started again and she sent me a big message saying she was so sorry and that she knows I didn’t cheat and that she wants to get back together.

We started talking again and she asked her mom how she would feel about us getting back together and her mom said she wouldn’t want us to. Since then we’ve been kind of sneaking around and talking while trying to have them not find out. It’s making it hard because we can’t talk very often. What should we do to try and convince them that we would be good for each other.

TL;DR me and my ex are trying to get back together but her parents don’t want us to because of what happened at the end of our relationship and after it