Sorry to hear your story AmbivalentOne!
Here are my thoughts on this:
She has been lying and cheating for a significant period of time but what stands out here is the utter disrespect and contempt she seemed to have for the marriage and you - that in itself (as far as I am concerned) is way more than enough to confirm that this marriage isnt a marriage and is well and truly over. However, you need to come to that conclusion on your own. Amongst her contemptible actions are:
Fvcking this guy in your home and even worse, in your marital bed!
Making fun of your job when you worked so hard to keep her lazy arse in a comfortable stay at home role.
Making fun of you physically.
Making fun of your personality and calling you too dumb to even know.
Praising his dick over yours and disparaging you here (talk about hitting a man where it hurts).
Being more than ready to chuck her family and marriage away for a piece of dick!
All of this says to me that there is no coming back from this. And all this for no apparent reason and now suddenly she is OK with you and your ugly self, small dick, stupid mind, bad job etc !?!?!?!?!
So ...
You need to plan this like Desert Storm and when you are ready go scorched earth on her!
She is the enemy not your imaginary wife (yes, you imagined her all this time). I agree with those that say
dont expose yet - wait until your legal ducks are in a row and you have done as much investigation as possible including VARs. The VARs may not reveal anything until you expose - that is when she may try to contact him.
when you do expose - do it piecemeal and see what she says at each stage. It will be infinitely more satisfying and effective if she gives you info that you dont already have because she doesnt know what you already know and what you have (dont show your hand). As somebody else said, show her the first picture and ask her to explain. Then the second one and again see what she says. Watch her thinking on her feet (and chuckle to yourself). Then show her a more risque photo and see what she says then. Eventually she will throw herself at your mercy OR attack you and blame you all for this. In any case you need to be clear with your next steps at this stage. Try early on in the process to get his full name and details if possible.
Then you go into negotiation mode and offer her a way out for less exposure i.e. if she gives you an amicable divorce you will go easy on the details you give others including your daughters. Remember she showed you no mercy early on. Have an agreement ready for her to sign at this stage (be ready to strike while she is still dizzy from your confrontation).
And as others are saying, and this is important, take care of yourself. Eat well, drink water, exercise and do the 180 to help your mind heal. Stay close to your kids and be ready to give them some version of the truth at very short notice (and I say some version to spare them the trauma).
As a reminder for me, when did you estimate this started and ended ? It would also at some stage be interesting to get her final version of why she did it (there will be many versions of this along with her many versions of the truth as you progress through with the confrontation).
Good luck and stay strong!"