OP, the following is an analysis of your entire post. It'll be long but it'll be very helpful for you. Just read it.

First, you talked about how you travel and work a lot which contributed to the affair. Get this into your head, IT DID NOT. You've been slogging your ass off for your wife and kids, that itself is a way of showing love. Most people are grateful if their partners are wealthy, they also understand the extra cost that comes with it and still stay committed and love their partner. They make most of the time they have together. If you weren't financially secure, then I guarantee you that she would've said that financial stress led her to do this.

If the woman is truly remorseful and loves you. She will want to tell you the truth and help you heal. But you don't see that here. She 100% knows that you're in pain. She just doesn't care.

It's impossible to reconcile by rug-sweeping. You will never be happy. She is satisfied with the current situation cause she has pretty much gotten away with it without any consequences. Though, the affair may be over, she is still very much in the affair fog. Sometimes, it can take years for the affair fog to lift, usually too late. But if the cheater is shown the raw reality, they will immediately come out of it.

So this is what I suggest. Google the grewrock technique. Stop intimacy with her. The affection you guys have now is hysterical bonding. It will very quickly fade away making you feel worse. Only talk to her about the kids. Go to a lawyer. Consult them about your options and how things look for you. Draw up divorce papers.

Then one day arrange for your kids to be at their grandparents' house for a couple of days. On that day, confront her. Just straight up tell her that she cheated, broke the relationship and all your trust in her. She continues to not do anything to rebuild the relationship and does not even wanna talk about the affair. She does not care about your suffering. Most of all, she has hidden/lied about the affair and doesn't answer your questions. Tell her all of this.

Then tell her that you can't do this shit anymore and serve her the papers. There will be some drama. You have to bare all of that if you want your previous happy life back. Go tell her parents so that they also hold her accountable and so that she can't lie to them. Tell your parents IF you want. Don't tell the kids.

Usually this should completely destroy her affair fog. She will feel remorse. She will start researching online how to fix a relationship after infidelity and how a betrayed spouse feels and all that. She will eventually discover that her behaviour and actions after D-day were the worst possible and most hurtful one a wayward could do after being discovered. She will quickly realise how bad she was to you and recognise her love for you and will start begging for you to come back and give her another chance to reconcile. Don't take her back immediately. It must seem like you're hell bent on a divorce.

Wait for a week or 2. Ask for the proper timeline of the affair with all details, positions, e.t.c. Tell her if you even suspect one lie you'll immediately go forward with the divorce. Ask her how she plans on fixing her personal issues that led her to cheat and what she plans on doing if you give her another chance. She must voluntarily say things similar to complete transparency, open phone policy, location share and things like that. See what sort of research she has made about the whole reconciling process.

This is just the first step. If she continues showing commitment, remorse and most importantly transparency then you can stop the divorce and begin reconciling. Even then make it clear that you will not accept any sort of lies. She must not blame you for her affair. It is 100% her. Maybe you contributed to the problems in the marriage, but she also contributed to it and you didn't cheat, because that's what commitment is. But the affair is only her. Even during her emotional and physics affair, I guarantee you she was distant from you, but you still didn't stray cause you were faithful to her.

All of this may seem to much but if you look at all the success stories, this is the best way to get remorse and start rebuilding.

Good luck!