Please slow down. You’ve had 14 years together. For you to be so devastated suggests to me that there may be other red flags you’ve been ignoring. Another possibility is that you are way over-reacting. Having some fun while on a work trip isn’t necessarily cheating. It may be that it’s just as he says. On the other hand, maybe he was having doubts about your relationship at the time and was trying out what it would be like with someone else. If so, he got his answer. He stayed with you and married you.
The question for you, then, is whether the last 8 years including 4 in a committed marriage outweighs a possibly dishonest weekend. A situation like this can deepen or break an otherwise good relationship.
It depends entirely on what the two of you do next. If you can talk about it openly, honestly and calmly, you may learn important things about each other and your relationship. If your discussion degenerates into accusations, defensiveness and counter accusations, it can result in a very deep wedge developing between you. I hope the two of you can take a big step back from the emotional first responses and instead talk seriously with each other about what your 14 years mean to you and what to do now.
He can’t undo the weekend. But he can apologize. And both of you can reaffirm the value of a shared life of 14 years. If there are problems in the relationship the two of you have been ignoring, this is the opportunity to work on them. If you find that you are unable to do that on your own, I hope you will make an appointment with a couples counselor for some guidance.
I wish you well.