Grneyes,
Welcome to MB although I'm sorry for the reasons that brought you here. But you will be supported & encouraged by those here to try to save your M if that's what you choose. Some questions so we're better able to help you:
How long ago did he ask for a D (divorce)?
How long ago did you find out he's been talking to this OW (other woman)?
How long have you been M'd (married)? It doesn't sound like you've been M'd that long.
You say he met her when you were on vacation? I bet that's when this started & he asked you for a D after you came home.
I've tried the begging....I've tried the pleading....how will he ever be open to listening to reason with her around?
Begging, pleading, won't work. Believe me, I tried too at the beginning. Every BS does. However, there are the Plan A & B in place by Dr. Harley that has been successful in breaking up A's (affairs) in many M's. Your H (husband) is in what's called an EA (emotional affair). Right now it hasn't progressed physically, but your next question, "How will he be open to listening...." has an easy answer -- He won't. As long as the OW is there disrupting things, he will not even consider working on this M.
Please read up on Plan A & Plan B. They are very useful tools. My H had an A for 7 months, we were seperated for 4 of those months & we are now in recovery. I've also had the experience of him telling me right in the eye that he hated me & he would never come back. That turned out to not be true.
Right now you can expect withdrawal from him while he's in this EA, but w/some work on your part, doing an effective Plan A for the next few months, you can try to break up the EA & turn his attention back toward your M.