I think a split of your finances is an excellent idea. I'm just trying to get you to AUGMENT it by taking one or two SPECIFIC things, things that enable her affair, to let her know that you will NO LONGER BE PAYING FOR. Cellphones are the logical choice, but you can also do it with an internet provider (if she's using the home computer to communicate with OM), plastic/cosmetic surgery payments, lingeries, professional hair coloring, etc.
I think you should go COMPLETELY dark while you're gone. But tell her in a way that you are just INFORMING her, NOT looking for some response out of her. "Just so you know, I will be unable to be reached while I'm gone. If there's an emergency, you can leave a message with (so-and-so)." If she asks you why, just say "I have some decisions I need to make."