What would you do if you catch someone cheating on you red handed at a public place?

I would just leave them, I would let them know why and for what reasons I was leaving them. But really what I would like to do, could not be done legally or morally. And to cause a scene in public may seem fun, but it is not fair to the other people around who simply want to relax and enjoy the day.

I would go absolutely mental and make sure they knew i saw them.

Punch him in the face

Make a scene! Humiliate them, then you dont need to get revenge any other way.