TorontoGuy: I echo everything Bigger already mentioned, and I would like to add a few things....
Firstly, we all understand what an incredibly hard time you are going through now and the tough decisions you need to make. The problem with A's early on is that emotions are so raw it's incredibly hard to do what needs to be done and/or even to figure out what should be done.
I read your other posts and understand you work a lot. DO NOT let anyone make you feel you are partially to blame for your WW's decision to step outside the M. I'm sure you've been told that because you work so many hours (especially with your profession, as only other Canadian's may understand just how much pressure there is on our MD's nowadays) your WW was lonely and the implication is her A is partly your fault...along with a slew of other excuses. You both may have contributed to problems in the M but there isn't anything you did that justifies her having an A, or her needing to have an 'open' M.
Although your WW appears to have admitted 'flirting' with her AP to you first in hopes of your blessing for her desire to take it further, chances are the A has been much more involved and ongoing than she has indicated. Your reaction was not what she hoped for and it's highly unlikely that she went NC and at this point she likely has no plans whatsoever to go NC, but instead they will take the A further 'underground'. Her ultimate threat that your M is over if you contact the AP's BS only supports this assumption, because if you follow through you really do pose a threat to her A by forcing her AP to deal with the fallout on his end which will also result in his having to choose his own M over that of any R with your WW. At this point your WW may not be confident of her R with the AP and she is probably afraid that he will throw her under the bus and the A will be over if it is exposed. Furthermore, your WW has no right whatsoever to give you an ultimatum about this. Whether she argues that it should be kept private to save yours, hers, or the AP's reputation or some other excuse, the fact is this is the consequence of stepping outside the M, made worse by becoming involved with someone else who is M, and that BS has the right to know. IMHO, you owe it to the other BS to inform her everything you know A related.
I hope you follow through with this. Regardless of the outcome, I'm certain you will regret not doing so in time. What the other BS does with the info afterwards is up to her, but most times the other BS appreciates this and often, including in my own case, both BS's tend to stay in contact afterwards and share information which is beneficial to each other.
Afterwards, expect your WW to explode in anger as she will at first feel you are robbing her of her one true chance at real happiness (although she won't admit this, at least right away). She may look like, act like, and feel like the W you have always known and loved but trust us, you most likely will see a new side to her you NEVER would expect! As if she has been possessed by an evil spirit or some kind of alien. Some call this being in "the fog". I highly, highly recommend you buy a VAR (voice activated recorder) and keep it hidden on you during any interactions with her for the next little while. The reason for this is because once the A is exposed, both your WW and her AP will be faced with the decision of continuing on or not. If they decide to try, it is simply amazing the things a WS will suddenly do and the accusations and marital history rewriting they will suddenly espouse. You need to protect yourself!
It must be incredibly hard for you to focus at work during all of this and if possible at all, you should consider taking some time off or reducing your work load. The separation arrangement you currently have sounds very reasonable and you absolutely cannot sacrifice anytime with your children. They need you now as this will be very difficult on them even if it doesn't appear to be. Also, if your WW can demonstrate that she is caring for the children more than you she could be considered the primary caregiver, given exclusive use of your home, and you could be relegated to visits with your children much less than 50/50. In Canada, whichever parent has the children 60% of the time or more is considered the primary caregiver and awarded full child support payments as dictated by the federal guidelines. It does not matter how you ended up S or D whatsoever. You most likely will be ordered to pay spousal support on top of this....and before you realize it you will find yourself paying her a huge amount of money to live in your home with your children, made worse by the fact she could even move the AP in, while you have to find a new place to live and you suddenly find you have far less time with your children than you would like.
It's very hard right now but everything you do is so crucial and you need to take charge....don't wait for her to decide whether the 'grass is greener' on the other side or not. As others have said, and you yourself have indicated you wish to do, inform the other BS what you know and then at least seek legal counsel if not outright start the D process (you can always cancel). Under no circumstances do you let your WW dictate to you any terms. She needs to realize her M is hanging on by a very delicate thread now because of her actions and she should be doing everything possible to salvage it. If she's not willing to, as hard as it will be for you, you must consider your M dead. DO NOT let her rugsweep the A or downplay how serious this is nor attempt to keep this 'private' for her. As many of us can attest to, she will continue in her A or she will eventually have a new one.
Sorry for the long post and for possibly sounding harsh too. I only wish I knew what I know now when I was in your position and if you have any other questions or want to discuss anything privately, please feel free to private message me too. Good luck TorontoGuy....you will get through this.