I'm going to cheat on a girl who's cheating on me at the same time
Why would you make it complicated?
Karma is a bitch. It's been done to me for a long time
Two wrongs don't make a right when you cheat on a girl who was unfaithful to you. Cheating is incorrect no matter who does it. You will only create even more Karma when you cheat on her.
That's unfortunate.
Just end it and find someone new. Cheater will always be a cheater, so don't take that road.