For the record I think people who cheat are disgusting human beings and I don't support what they do in any way shape or form. They will be accountable for their actions before Christ's judgment seat, but just remember before you take too much pleasure in that - so will everyone else. My sin nailed my savior to a cross in violent and painful fashion.
All this being said, I'm confused (and a bit concerned) by your requests about whether or not it's okay to punish someone who cheated.
Define punish?
Punish as in get divorced and sue for alimony? Or punish as in bash in their car with a baseball bat, destroy the cell phone they used to text their lover, or plaster what they did all over facebook and bring it in front of their boss at work.
If it's the divorce thing, then yeah - you can do that as adultery is biblical grounds for a divorce. If it's the other stuff, then no - act like an adult, and don't break the law just because someone has wronged you. Vandalism is a crime, and so is character assassination (you could be sued for libel).
And it's sad you're going through this. God can use the actions of the unrighteous for good, even if it may not seem like it right now, and even if we never understand during our life time.