As several have already said, unhinged arguments in front of the kids is not healthy for them - or for you.
Your anguish, pain, and anger are well understood and all of us here have felt what you are feeling.
Your wife, if she even has the ability, should be able to understand your anger, pain, and lashing out with those detailed comments that are meant to expose and embarrass her.
They are the result of the pain you feel from being betrayed, being deceived, being lied to, and her using your trust in her to get away with it all.
The willing betrayal of trust is the greatest sin of all sins and the greatest wrong of all wrongs.
And it hurts beyond words when that betrayal is from the very one who gave the greatest vow of trust to our very eyes.
The barbed comments she made to you about the sex with the POS guy were said out of her anger for the following reason:
She got caught.
She got caught by the very person who was never supposed to find out.
She got caught doing and being the very opposite of the most solemn vows she ever gave in her life.
And by betraying the greatest vows one ever makes in their one life they have here, she now feels even more empty and invalidated than ever before.
The fact that her affair with this person was nothing more than a hopeless attempt to garner some sense of validation-thru-sex-for-praise is now exposed as an empty, pathetic, and humiliating act.
That is an immense amount of personal failure to face for some one who does things like this so they don’t have to face themselves and their personal failures.
Based on reading this thread, I can confidently say my XWW acted almost identically to how your WW is acting.
I wish I was able to give you advice to somehow get her to “See the light”.
Unfortunately, there is no such advice.
There isn’t any because none of what she has done has anything to do with you or your marriage.
There is really nothing you can do to “open her eyes” or have a “come to Jesus” moment where she clearly sees how horrifically she has been acting and how it has affected the very people she vowed to care for and protect the most.
Only she can do that.
Now, you must ask yourself how long you want to wait or if you are willing to wait at all for her to “come to reality” and see what she has done.
Some realize it right away after being caught, some take a while before they see the truth of themselves, and some will cling to excuses and blameshifting for the rest of their lives.
I’m seven years from divorce being final, my XWW is remarried, and she is the same contempt-filled, blameshifting, emotionally-immature victim she has always been.
She has never even apologized to our children for anything.
There is nothing within her that will ever get her beyond the excuses, blaming, and reactionary anger when in a position where she has to face herself and her behavior.
It was much easier for me to think of mine and my kids future and make decisions when I came to the realization that there was simply nothing I could do to get my XWW to see herself because she did not want to see herself.
My suggestion is to start thinking in those terms where your WW’s irrational attitude is not something you can change.
The ONLY thing you CAN change is what YOU are willing to tolerate or accept or not tolerate or accept.
All the arguments and hurtful words are not going to make you, or her, feel any better nor get you anywhere outside of this.