Yoyob,
It often appears like the majority of people posting here are quite harsh in their response to something as devastating as has happened to you. Some of the reasons for that have already been shared with you but I think it is important for you to filter out and get what you need from the site.
On the flip side, there are a number of stories here about people who reconciled successfully. That seems to be what you desire, if possible. And there are a number of people here who have proven that this is not only possible but an outcome that you can strive for and be truly successful with. I think that despite people here posting harshly everyone wants the best for you. And there are people here who, knowing you want to reconcile, hope that it is successful for you and your wife. I am one of those people but I am certainly not alone.
A lot of people in your thread have also told you that true reconciliation where the marriage actually recovers takes a lot of work and effort. Many describe it as the first marriage ends and you have to work to create a new marriage. I think that may be less of the case after a ONS but in your circumstance, with a one-year long affair, it may really take the recreation of your marriage to succeed.
It is clear that some people here have misinterpreted what you have written either because they look at everything through their own set of experiences or because, perhaps, you did not explain everything you were thinking and feeling up front. But push those things aside and look for the sound principles which are articulated so well here in the tools in the healing library and in many experienced people's posts.
Some of these principles include: avoid any type of rug sweeping at all costs--- which holds both of you accountable for real and valuable changes that need to occur to protect the marriage in the future, establish NC and full transparency of communication, seek out thorough individual therapy for both the WS and the BS (usually before investing in a lot of MC), make sure the WS understands what it takes to heal you and is willing to do the work on both herself and you, avoid jumping straight to reconciliation until some of the hard work has been done.
Despite what is a devastating experience of a year-long affair it does seem like there are a few rays of sunshine. These include the fact that your wife confessed quickly, the fact that the messages you have read show no signs of this being an exit affair, the A ended on its own and that you have stated she seems to be showing remorse. You can and should take hope from these signals.
At the same time you are taking Hope from those signals though, you would be wise to follow the principles of true reconciliation mentioned above. Trust but verify. Be hopeful but also be realistic. We are seeing the hope in your words and that is a good thing. We are also seeing pieces of realism as well. Even though I hope you could reconcile, if that is your desire, I still have some concern based upon how you have represented what is happening. Some of my concerns are similar to others who have posted earlier. They include not seeing a lot of description about your wife's possible remorse. Not seeing NC, in any way, being established. The feeling like your wife has not been fully held accountable. The possibility that you are jumping too quickly into reconciliation and MC without some of the fundamental work being done first, particularly by your wife.
I know that some of these things are under way and it is impossible to share all of the details with us. But there is still a sense that you are not working the fundamentals that will lead to True success. Take NC as an example. If she doesn't establish no contact then you will possibly be triggered every single time she goes to work. Just when you think you are feeling better something will happen with how she dresses in the morning and she will go off to work and you will be wondering is she taking a long lunch with the boss again.
I hope you can see how that one principle of NC is designed not to punish her but to hold her accountable, to protect your marriage moving forward, and to protect you. BS who are triggered consistently is essentially universal in infidelity. And you are setting yourself up to be triggered consistently in a never-ending pattern unless something changes. We all realize that quitting a job as a middle manager can have a significant impact economically. But not addressing the frequent contact with her boss is asking for a failed reconciliation.
And this connects to some of the people telling you to see a lawyer. Because her AP is the senior executive in the company there may be legal options for her to leave the job and be compensated for the disruption in her earnings. A lawyer won't force you to do that but talking to one would give you insight, information and understanding of your options.
I feel for you and really hope you get through this. I want you to be successful with reconciliation if that is what you really want. But to do that, it is wise to consider the well-worn path that is described so well here in the healing Library and hopefully adopt a few more of the key steps than you are now. Skipping over them will not help you, it will not help your wife, and it will not help your children grow up with parents who are in a strong loving marriage. There is a lot at stake and I know you are making progress locally, which is excellent.
Please also consider some of the more experienced and thoughtful voices here (most far better than mine) as good and well-intentioned counsel on this most difficult Journey.