Thirteen years is a very long time. By now you know every relationship has roadblocks and pitfalls that must be overcome and it's not usually easy. This sounds like a bigger than usual one for you.

Speaking as a guy, I'd be humiliated if my girlfriend slapped me. I'd be mad and treat her coldly for a day, maybe two or three. It wouldn't be a cause to break off the relationship unless I had already decided beforehand to do so and was simply waiting for an appropriate time.

You are jelous of his relationship. You confronted him about it and you don't believe his denials.

My main concern would be to prevent your belief that's he's going to leave you to become a self-fulfilling prophecy. A running day-after-day arguement or simply dumping him outright could do this. I like to believe true love exists and hate to see long term seemingly successful relationships fail.

He does owe you more openness regarding where your relationship stands. Create opportunities for him to give this to you, such as a late night dinner at a fancy restaurant or some other unusual date-like atmosphere where you two can talk further.