I'm the other man.
I'm shocked. Why are you cheating on with someone that's already in a relationship?
Cause my woman isn't sleeping with me.
Just because your partner is not having sex with you does not give you an excuse to cheat on them, especially not with someone else in a relationship. You are ruining the lives of three other people by doing what you are doing. If you are unhappy in your current relationship, talk to your partner about the issues.
I'm a commitment phobic.
If you are afraid of commitments, then you should strive to fix it, not try to have other relationships with other people that are already taken. I suggest you end your other relationship and focus with your wife and see how you can be back with having an intimate relationship with her, or how to properly end it if you are really having trouble with commitment.