If she cheated and is genuinely sorry, then yes you can contact her if you want to. But if she's playing mind games, then don't contact her. Anyone who is playing mind games with you, especially if they're your ex, already has questionable credibility and really isn't worth your time. Also you seem like you're very much ready to move on and contacting your ex will prevent you from getting the clean get away you deserve after she has cheated on you.
I know that you probably still have some feelings for her and it's normal, even if she did cheat on you and is playing mind games with you. I mean I still have some feelings for my ex so I would know! My ex ended up being a jerk who was just using me and now seems to be playing mind games with me, texting me and trying to talk to me when he explicitly told me that he never wanted to speak to me again. An outsider to my situation would think I was crazy to still have some feelings for a guy like that, but I do and it's okay. So don't think that still having some feelings for your ex is stupid because it's perfectly normal to do so since you were once involved with her. The more experience I gain, the more I start to believe the saying that once you love someone, you never really stop loving them completely.
Even with that, it doesn't mean that it's impossible to move on. You can still have some sort of feeling for them, but have already moved on. I know, it's pretty contradictory but it's true. The first step is to know and accept that you deserve so much better than someone who treated you poorly and is now playing with you. The hardest part to this is accepting it. You may know all about it but deep down, you may not have accepted it quite yet. Are you really able to find someone better? Can you really find someone who will love you like your ex did? Can you love someone else just as much as you had loved your ex? Could someone better possibly love you? Once you can answer those questions with a confident yes or feel indifferent about those questions with no conflicting answers, you'll know that you have accepted it. To be able to accept this easier, try to cut off as many ties as you can with your ex. For instance, I don't text my ex back or talk to him unless I have to (and only for reasons that concern the club we're both in) and it has helped me do some immense healing.
That's why you should try doing the same thing if you truly want to move on from her. Give her the cold shoulder and try doing things that make you feel good about yourself. Ignore the fact that she's trying to play games with you and tell yourself that you deserve better. Responding to her and her games will only feed her ego and give her the power to control your happiness. Don't give her that power. As tempting as it is to fall for those games and talk to her again, don't do it. You want to move forward, not backward. And after you start to stand up for yourself more and more, you will begin to feel empowered. It starts to feel good that you can leave your ex in the dust and hold your head high. At first, it won't be easy by all means and it takes time but you'll eventually get there.
Anyway, I wish you luck!