I cannot say if I believe or not that this guy is the whole reason for this. I think she may have been considering and drifting before she decided to start something with him - even as far back as just going to school. Just seems to me she was pursuing things and getting ready for her departure by getting a degree, getting herself prepared job wise and all. I have been through things not entirely different from yours but I understand and I know how it feels. of course my ex and I had never fully gotten on well so it's probably not as shocking to me when it happened as it may be to you right now.
Yes later the other men came into my situation but truth is I only say that to underscore that her emotional affair with him is just a symptom of what may have been more her just not being entirely there for you anymore.
This is all on her though. Regardless of the reasons she uses to make excuses for why she has left, the fact is, she chose not to put anything more into the marriage and be the wife any longer. Stand strong in that you may have made mistakes but it seems to me, that you at least remained committed.
As for the kids, they will be alright, albeit it does hurt them, this is not about them entirely, the mom hopefully will keep being mom just like you will keep being dad. Its hard on them but as a father of two boys that are now teens, for the most part I have done what I can as a single father (even being sole parent for nearly 4 yrs) and they are ok as they can be (as teens can be anyway lol). You support and be there for the kids and try to remind them that their mother will always be their mother so they haven't lost anyting in that manner.
Find your own independence, you can. I did. You have some very hard days, weeks and maybe months ahead, I won't lie but you can do this. don't let it break you or make you feel worthless, you aren't. Even the best of people are betrayed at times in their lives and it hurts but it's not their fault, it's the cheaters' fault.
take heart, there is hope and it is not just an end you are facing but a new phase in life too.