I'm not familiar to the inclusion of infidelity, however, I am to the marrying for the wrong reasons. And since that is what you've said you've done, (marrying for the wrong reasons, and especially with fighting all the time, to the point of abusiveness), then chances are likely that your marriage will eventually reach an end.

The fact that you cannot overcome the idea of him cheating on you is what's basing your present emotional status. He wont share with you what you need most TO put this to a rest, therefore, I don't really see much relief for you in your present situation, unless you allow yourself TO get past this on your own, which doesn't seem likely.

I'm sorry you're going through this, but it seems to me that you really only have 1 of 2 choices: Either accept the fact that he isn't willing to help you through this and overcome his infidelity on your own in order to remain, or leave.
I realize that sounds easier than done. It boils down to how much you are willing to do for your own self, as he certainly doesn't seem concerned with helping you at your time of need.
Don't ever think that you HAVE to remain in an abusive situation. Do what's best for you.

I hope this works out for you. Good luck.

Shangrala