Yes...your wife is very vested in keeping the friendship and her daily relationship with you and the kids intact.
Divorce doesn't work like that.
If you want to give her a sample of what life will really be like plan, without giving her notice or "at the last moment" a camping trip or something like that with the kids. You want to go somewhere that basically you'll be completely out of touch for 2 days. It would be great if it was a couple days that she was off work and having to sit around idle wondering about the good time you were having and what the kids were doing.
Take your phone but let her know it's a technology free weekend and you'll be turning it off (because there is no cell service anyway) and you'll be checking in on Sunday while driving home.
Might be kind of hard to take a 1 year old camping but come up with something where you just have no cell service.
By doing it last minute she'll also wonder if there's someone special with you or that you're maybe meeting up with. Let her wonder. Might even be funny to ask some strangers to take pictures of you and the kids and let her wonder about who's running the camera again.
Your wife really isn't understanding the full consequences of her choices. Once this divorce process gets more acrimonious this little "trip" might not work as well.
Also...will switching to the day shift at the same hospital really help? OM still works there. She could just be switching to a group of co-workers naive about her "special relationship" with Dr. OM. You'll never know. Discuss if you can with her the concept of "getting a fresh start" and whether that can ideally be achieved by just switching floors and shifts. Why not...AT THE SAME TIME...apply for other positions at other hospitals, clinics, etc. She may be surprised to find something better and more ideal for a soon to be divorced single mom. Why not apply to numerous places?
This could also parlay into a discussion about why not BOTH of you get a fresh start somewhere else? Divorced or not...you could both move across town or out of state. You also aren't exactly thrilled with everyone knowing you couldn't satisfy your wife and she cheated on you (I'm purposefully suggesting saying that not because it's the least bit true ...afffairs aren't about the BS...I suggest it solely because it MAY stoke an empathy response from your wife whereby she has to say things like "that's not true dear you were a wonderful husband and lover" and gives her a window into the fact you are not some emotionless stoic man).
One of your wife's remaining primary objections seems to be associated with her feelings of loss of her integrity and not being about to face a life with you (and, presumably your friends and family). Have any of your friends gone through this?? They may not say it but have any reached out to you and have been more supportive than the others? They could be a couple that's already recovered and the wife might be a good candidate to talk to your wife and explain that although she's done an awful thing, that her reputation can be restored and her integrity and self worth reclaimed depending on how she reacts, changes and makes amends for those mistakes. Her [wayward] actions may define her NOW as she is in the midst of the behavior but if she changes her course of action then her [repentant] actions (contrition, retribution, accepting responsibility, seeking forgiveness) will THEN define her as (once again) a kind, decent, redeemed, holy person who lost their moral and ethical bearings for a stretch of time.
She's NOT the only person in the world that has sinned gravely. There is a path to regaining her integrity; however, that path doesn't involve wayward unjustified divorce.
The internet is 90% complaining and entitlement and I hate it because I deserve better!