The fact that she was hiding OM means that at least she understands that it is probably not "OK" and admitted she thought you'd be upset about it.
I can say that many here who have discovered an EA, worry it will turn to a PA. Even though, for many, an EA is just as bad and painful as a PA, as discovered and reported by psychologists.
That said, there is no guarantee that trying to stop the A will have that affect. In some instances, it can push the A further underground and even speed the affair spouse further into the A.
Best for you to do is accept that it is happening and... if it is not a deal breaker for you... let it run it's course, become a man that only a fool would leave, and stop snooping or pressuring your W directly. The quicker and more permanently you can make this awesome changes in yourself, the better. But... do them because you want to make these changes in yourself, for your future, regardless of whether your M is saved, or not.
An A often runs it's course, regardless of EA or PA, and will fizzle out, eventually. The less you provide a reason for her to run FROM you (are less attractive option, in her mind, not necessarily a reality), the sooner she will have an opportunity (reason) to choose to return to the M and work things out.
Remember, an A is a symptom, so there is some reason why she sought the OM. ie. Something she wasn't getting from you. Of course, she does not WANT that from you right now, so you will have to find other ways to be attractive to your W... or if the M is not saved... any future R.
