After the success of my last personal problem answer:
First though, even if his explanation is true, he let it get to the stage where it was a problem, I don't think he has much of a case in keeping the relationship at a stage here "she has read too much into it" and "her family are overjoyed she has met him" going any longer than necessary. I'd have thought a frank talk would not take too long. Whenever it ended, the fact that he'd have to see her at work isn't going to change is it ?
I suspect you are a little more trusting than you could be in the circumstances you describe, what with the reluctance to do something about it, but who knows, maybe your relationship is the exception.
Indeed being apart may help clarify things. But I'm more suspicious that the suggestion it is being used to put off having to do anything. I'd suggest putting a time limit on it. Or getting an understanding that a split is only going to help once he has sorted this other relationship.
If I am honest the situation does not sound good, and maybe heading for a clear break, but in any case it is presently his responsibility to move things on, and if he doesn't, then take the lead yourself and move on.