I think my wife hooked up when we were separated
What led you to believe this?
I have been dating her since high school and she is always friendly with random guy that I've never seen.
You cannot blame your wife for doing what she wants when you are on a break. If you feel insecure you should ask her and if you don't like the answer you may need to leave and move on.
It's evident that she has been cheating on me since we broke up
If you are already separated it sounds like she has moved on. Maybe you should too? She can't be cheating on you if you are not together.