SS, sorry about your situation.
I agree with K9 - you are not the man she respects, nor are you the man she wants to fight for. You are the back-up plan, the comfort zone, in case the AP is not willing to take their relationship further.
Your wife has bailed on your marriage for some time. She even bailed on her kids and your Xmas traditions, in order to be with this guy.
She has such disrespect for you that she takes him on your special intimate vacation. You have read where she mocks you with him, she has totally played you while she lives her exciting fantasy with her new found best love of her life. She lies to you continuously, she has no connection to her vows, to you and is happy to risk it all for this AP.
All your beautiful comments about how much you love, and connect with your wife, is how she feels about the AP, not you.
The sadness is that she did this with total disregard for you, the person who stood by her, who waited in hopes of being intimate again. You never had a chance, as many of us where we are totally blindsided.
You've been nice, supportive, and understanding for the past 6 years. It has not kept your wife in the marriage. Therefore, to continue a soft and nice approach is not going to bring her back either. She doesn't share those feelings for you, they are suppressed under her excitement for the AP.
As others have said, look out for yourself, you've done the STD tests, now get the legal stuff going. File for divorce and show your wife that you are not willing to share her with anyone. Seek legal advice to protect yourself and your kids. Do not leave your house again, your kids need you there and you are not the one to leave the marriage.
Respect yourself, wake her up to the new reality, show her the door. This is an ideal time to have her things packed so when she arrives, she must find a place to stay. The shock of taking her comfort away can hopefully awaken her situation she has created.
Let her do the work if she wants the marriage to work. Right now she is only kind of sorry for being caught.
Good luck, you are in for a very rough emotional ride. Get help, professional and close family ties.