Hell. No. His behavior is NOT OK. And neither is hers. BY ANY STRETCH.
You're too controlling and don't have enough friends? Guess what? The remedy to that is not for him to have a different girl "friend" who refuses to be nice to you, the remedy is for you and he to start going out more with other people together and make new friends. Which he should support you in doing and even help make the plans if you're not a natural social butterfly.
You are COMPLETELY justified in all of your feelings. THEY ARE SO WAY OUT OF LINE I CAN'T EVEN BELIEVE A COUNSELOR HAS NOT SLAPPED SOME SENSE INTO HIM. My ex and I tried for a while to rectify our situation before I knew he was cheating like crazy, my only beef at the time was that he had so many female friends who wouldn't acknowledge my existence, and the first thing SEVERAL COUNSELORS TOLD HIM was that he had to stop being every other woman's best friend but mine. Any time spent with these other "friends" was basically time spent eroding our relationship.
He does not need to sit over drinks and talk about life with any other woman. He just doesn't. Unless there is a completely undeniably platonic dynamic and she is RESPECTFUL OF YOU. This is not some anonymous married platonic lady he sees on a business trip who obviously doesn't know you where only a rabid intentional cheater would "let something happen", it's someone he works with. She's friends with you-or at least not intentionally NOT fiends with you- or there's a problem with her. That is a standard boundary.
But you know all of this.
The problem is that now you are in scared mode, checking his texts, trying to lay down boundaries and it all just makes you the bad guy unfairly. He has put you in this position in collusion with this nasty woman. Good women do not act this way. I have tons of male friends and NO relationships like this with men who are attached. I am friends with the female first, the man second-even if I've known the man longer. Even if I'm closer to the male, I've at least TRIED numerous times to include the female and I always ask about her, and I behave in an appropriate manner. If I even suspect she may be uncomfortable with me, I steer clear form her man-aren't we all a little to busy for all this socializing outside of work as adults??! I would not be out to drinks with someone's husband all by himself on my birthday. WTH???!!!
What can you do about this travesty? Honestly, I think anything you do will make it worse at this point. The neediness. The snooping. The therapy. It all fuels his need for "an escape" and makes her seem like the better friend. They are such jerks for doing this and they probably feel like there is nothing wrong with it.
This may be impossible, but if it was at all doable, knowing what I know now about things like this (and I never would have said this 15 ears ago): I'd set him free with all the love in my heart. I'd say it was my problem not his, but I am very saddened by this outside friendship of his with a woman who refuses to acknowledge me. I don't want to hold him back in life or make him unhappy and I'm feeling bad about myself for not being social enough for him. I don't want to drag him down with therapy and stuff if what makes him happy is his role supporting this woman in her needs so I'd like a separation and could he please move out. Maybe we can work on things going forward if it's meant to be with the two of us. If he wants to consider therapy again or changing things I'm open, but I won't force him. Then it would be in his court to change or lose his family for this woman.
Why wait for a painful full-blown affair to go through the exact same damn thing?
I'm sure that's way too extreme for you, but honest, one very common alternative to that is that they continue to carry on like this, you continue to allow it, and things can only go downhill from there on every level.
All he really has to do is quit acting like this. Which is too difficult for him because of HER FEELINGS. And maybe his. That is NOT putting your marriage first. Any counselor would tell him that.