If what you want is for your wife to remove her head from her posterior and embrace the reality that she has created, and change her attitude to you, the most potent weapon in your arsenal is indifference.
Your wife has made a series of decisions that have resulted in her cheating, and beginning a life of living out of a suitcase for weeks on end, in one hotel/motel after another. Away from her home, and away from her children. How many people in their fifties would see that as a positive thing? The reason she keeps mentioning trying to save the marriage she fired a missile at is that she can see what a barren and empty life her decisions have created for her.
If you divorce her, how many options does she have? Spend the next decade with a small apartment that she calls home, while she travels from place to place by herself? Even if she thought that casual encounters with random strangers was the height of excitement, how many years can anyone do that without getting burnt out, and realizing that they are slow-moving, low-hanging fruit for any opportunist who can be bothered to buy them a drink and say whatever tried and tested generic lies are required to obtain free sex?
And what if her health fails? Who is going to look after her and visit her in hospital? Steve, who she spent a night with at The Lucky Horseshoe Motel in Flytrap, Arkansas? Or Dave - that was probably his name - from that drunken night at the Downtowner Motel in Toejam, Missouri? What about Phil, from the Sleep-E-Zee Motor Lodge in Armpit, Tennessee? Chances are, those knights of the road are going to be too busy to show up with chocolate, flowers, and a bunch of magazines for her to read.
What she is learning, from the new life she has created for herself, with no regard of what it might do to you or the kids, is that her version of 'independence' is actually a thinly-veiled version of 'alone in late middle-age', with a cancelled future.
Let her have a bucket-full of the new reality she has created for herself. Let her see what it really is. And what it is not.
Let her know that you are considering your options for the future, and that yes, the two of you can talk with some kind of mediator, but that you are also thinking about how your life could be if you were single. Let her know that life with her is not some kind of glittering prize that you cannot live without, and perhaps even suggest that perhaps she ought to give her life on the road more of a try before the two of you hold discussions.
Your value - and what makes you unique in the world - is that you give a damn about her. And her new reality life will force that point home for her, as she checks into one motel after another, and she starts to understand that the attention she may get from random strangers is not a validation of her 'hotness', but simply the stock actions of fishermen, repeating the same old ploys to see if any self-deluded fish are biting.
The way to get her to come back is to set her free. That does not mean divorce her. Rather, it means to encourage her - and you should do that - to enjoy her new life and new job. Tell her that she needs more time to spread her wings and grow into the job. Stand back. Step away. She is clearly already having doubts. Give those time to sink in, while you consider what you would do with your life if you were single. And let her know that you are doing that. She will be thinking about that when she checks into the Midway Motel in Buttcheek, Omaha, switches on the shower, and gets hit by cold water and a TV that does not work.
You need to understand that because you give a damn about her, you have a huge amount of value to her, because to the rest of the world, she is just another random stranger that they have no commitment to. And if you want her to change and become more proactive, let her know that - essentially - she has to pursue you again and make you believe that she has a genuine interest in you. This is not about you winning her back; it is about her winning you back. And she is going to struggle to do that while she is checked into The Ace of Spades Motel in Heatbump, Texas, putting her tights into the sink to soak for the night.
You are the prize. Her new life is the booby prize. Give her time to experience that. Give her time to see what she had, but took for granted. You don't know what you've got until you lose it.
Be detached and neutral, and see what happens. If she makes more effort, then it may be worth you reciprocating. If she does not, you should not chase her, because you will be wasting your time.
Our thoughts are with you.