Strength brother, it is tough, SI is here for you, you are not alone
I am sorry to say but parking lot sex forces me to look at her as some slut I never knew.
Reality check
What you did not know, but what you do know now, is that she cares more about herself than about you, and that should open your eyes. She is not your friend and she does not have your best interest or that of the family at heart, she is a selfish bitch that has betrayed you and will not hesitate to do so again if it would bring her any (meager) reward.
Action to take
That bitch left you in the cold. Now soldier on on your own with your kids soldier. If she does not care about, and for you, well to hell with her and YOU will. So from now on you should start doing things that are best for YOU. Be your own best friend from now on, the more you focus on YOU the less you focus on her (WW) and him (OM).
In the phase that you are currently in, that means you should seek for social support from your friends, telling people who you know or even random strangers what has happened to you - it is not your fault in any way, and you have nothing to be ashamed of - and they will offer their support and advice, reading all other posts and advice given here on SI to educate and empower yourself, securing your financial assets (e.g., pre-nup), doing the 180 (see healing library), understanding that you can ask 'why' until you go crazy but knowing that you will never have the 'why' because there is no 'why' and you can never verify, considering yourself a single man from now on, and so forth.
In a later phase, you can do things that make YOU HAPPY without her interference, such as buying that car or motorcycle you always wanted, going out and making new friends without her disapproval, eat whatever you like, and maybe even finding a new and better girlfriend or wife! Hey, not being married to her also has its benefits for you!
Seriously, this infidelity stuff is harmful to your mental and physical health, the more you focus on her the more you kill yourself while she is not worth killing yourself and your children need you, so focus on YOU. Be your own best friend.
Whatever happens, know that everything has changed now and things will never be the same, stay calm as much as possible (very important), avoid her as much as possible since she does not have your best interest at heart and will only bring you pain and trouble, be your own best friend, and stay posting here.
It sucks, but you have to just suck it up - and smile - and soldier on on your own now. YOU CAN DO IT!, be your own best friend!
I wish you well, strength brother, SI is here for you!