Should we break up? If so, how?

We've been together for over a year and I do enjoy spending my time with him. We can laugh together and we really have a good time.

However a few months back he got involved in things he shouldn't have. He started shoplifting with a 'friend'. They got caught and he's since stopped I believe. He also used to smoke weed with this friend and I feel as though his friend was just using him, even though he couldn't see that. He also lost my trust by messaging another girl, even though it was quite obvious they weren't going to meet up as he'd always arrange to meet her when he was seeing me and still see me. (Weird I guess?) We see each other every day so there's hardly time for him to see anyone else.

However my parents found out about all this and no longer trust him. He's not allowed around my house and I have no objects related to him in my room any more. A few weeks back they forced me to break up with him, I did but I didn't want to so we ended up back together. They weren't happy and I feel like I'm breaking my family apart and causing arguments all of the time, but I also feel as though it's his fault for being a sheep and copying his friend. He doesn't do any of that stuff now as far as I'm aware but my parents won't accept him. Can he ever get their trust back? If not, I don't think we can have a future together. I'm scared that my parents are going to be right about him, but he seems so caring and I love spending time with him. What should I do?