I'll separate the cheating discussion because I see it as a different issue than the one on the importance of sex. You have every right to divorce a cheater - that is your choice. I would not recommend staying with a cheater that you can't forgive and trust - you are just setting yourself up for more suffering in the future. (to be clear, I'm NOT saying you *should* trust him, he may not deserve it, just that you shouldn't stay with someone that you can't trust).
To be very clear: it is completely OK for you to not want sex because he cheated - but if that is the case, I don't think it makes much sense to stay together in a marriage that will never be happy - for your sake.
OK, on to sex: When you way that you do not enjoy sex, does he make every reasonable attempt to make it good for you? If not, then he needs to change is behavior - sex should be mutual, each trying to please the other.
If he does make the attempt but you still do not enjoy it, then its a very tricky situation. If you had an active sex life before you got married and early in the marriage, it is reasonable for him to expect that to continue if his behavior hasn't changed. Then I think you are left with a choice: Provide him with the sex that he wants even if you don't enjoy it, OR, allow an open marriage, OR make him feel free to leave so you can both find someone sexually compatible.
I don't think it is fair to make him feel he should live with a limited sex life if he had reason to expect otherwise when you were married. (again, this is IF he does his best to please you in bed)
He is never going to get over wanting sex. He may be willing to stop bugging you about it, but he will always be angry and resentful (even if he doesn't show it). He will very likely cheat again because he will feel that he has an excuse.
It seems to be that most have the opinion that sex is necessary in a relationship; while I can understand the importance of a healthy sexual relationship, what if the sex is unenjoyable? where its more about the other half instead of your needs? Such as my H, claims its all about me but it's not, it's about him and him getting his rocks off. Which is part of the problem for me. I personally haven't enjoyed sex in years, especially since I had kids. Before kids, no problem with it but after, no thanks.
For those asking about what he did, I came home from work early one day and he was home with another woman in the house, this was a little over a year ago. Over the past few years I have found evidence of him being online and doing things there, talking to other women and pictures of other women on his phone. I am aware that I should just leave, but yet part of me inside says I should stay (can't make sense of that honestly). It's not easy to make a decision that will change the rest of your life and change the life of your kids...........