If she's the one having an affair, why would YOU be the one to leave?
Please consult with a good family law attorney on this before leaving your home -- preferably one who specializes in "men's rights" and paternal custody issues. In many jurisdictions, your moving out could give your wife grounds for an "abandonment" charge against you.
In what ways are you "trying to improve the relationship?"
If she is having an affair, and YOU know that she's in contact with him, and SHE knows that YOU know, and then she sees you doing things that DB would consider "pursuit?" Attraction killer!
HINT: You should be working on things that improve YOU right now, NOT things that improve the relationship with your wife. At least not while she's wayward. There will be plenty of time for that later, if and when she decides she wants to commit back into the marriage.
With regards to the support, listen to what your attorney recommends.
As for what to tell your friends and relatives? You might at first just say that you are having "difficulties" and leave it at that. If things don't improve and you head for D, I'm a believer in telling the truth, not in covering up deceit with more lies.
Good for you for seeing and attorney. Put yourself back in a position of strength.
