It's good that you see these as mistakes. Security within a relationship is the greatest enabler for a wayward spouse to continue being one. Your efforts to pursue, show love, appreciation, etc. reinforced her willingness to remain in an affair. The opposite of this is indifference, which you can get to with time, and the sooner the better, as you will feel empowered and in control of your own destiny.
As hard as it to hear and believe, there's not much you can do, except focus on you, which inherently means less focus on her. To put it bluntly, I would file for divorce, focus on you and your kids and detach the best you can. Should she come around and you still want her, you can always stop the divorce. However, I wouldn't divorce for purposes of waking her up, but for the purpose of regaining your emotional health and that of your family by removing yourself and them from infidelity.
As long as you are with your wife, you and the family or in her web of infidelity. That's her issue, not yours and the kids should be as far removed from the limerence that she is is as possible. Yes, the kids are impacted, but as keepabuzz stated, a home in which infidelity exists and the dysfunction that come with is not a healthy option neither. Both parents being under the same roof, but not in a loving relationship can leave is as negatively impressionable as divorced parents can be.
Detachment is difficult, but gets easier each day where limited or no contact is the objective, even in the same house. This has happened to me twice (two fiance's), and the second time was much better than the first as I realized detachment and inward focus served me the best. Each day of limited to no contact strengthened my resolve. Days turned into weeks. Weeks turned into months. End of the first month, I was functioning at least. By the end of the 2nd month, I was returning back to normal. End of the 3rd month, I was nearly myself. By the 6th month I was ready to move on relationship wise and I was happy again.
Being happy again allowed me to see authentic happiness in others, which enabled me to meet and date my current wife of 20 years. In retrospect, the person I'm with is who I should have been with all along, but you couldn't have told me that during the time of my betrayal. Focus on you and your kids only. Currently, you are married in principle only, so by looking inward as opposed to outward to her and your marriage, you are simply taking a position that she has enabled. It takes two and right now, not only is she not close to being as one with you, but she actually wants to be with another man.
Again, I'd help expedite that and tell her to come get her clothes so that she can move in with him so that you and your kids can reclaim the family unity that will continue, with or without her. The sooner the better.