hey, To be honest you are more than within your right to go out with this guy. Ultimately you can decide who you want to go out with, not your mum. Your mum may not like it but that is the person you want to date. If she loves you she will accept that this relationship is going to happen.
I can understand her being a bit worried about giving him a second chance, because what he might have did the first time, but that is up to you if you make a mistake. You will learn from the situation. Maybe have a meal or something with your mum and potential boyfriend so that way your mum will know if he has changed.
As long as both of you want it to work then just go for it :)