Hi Lola,
I am so sorry you are here and find yourself in this devastating situation. SO sorry! Horrible, painful beyond belief.
I am writing to you because your question is also very close to my heart and i have a view which is not the norm on SI. I almost feel bad expressing my feelings and thoughts since I understand how many are passionately opposed to them, but at the same time I think it's important to speak one's thoughts, put other opinions out there and not just go with the herd.
I do not think the OBS always needs to know in any circumstance. Every situation is different and each person has to decide what is best in their own situation. There are many factors to consider, some of which you've mentioned, like innocent kids involved, ability of OBS to deal with devastation and if something really bad happened, how would you feel, sometimes your own safety or worry about other things. It's complex; people want to make it simple because it's easier, but it's not easy, at least i don't see it like that.
I also think that telling is opening up a Pandora's box, which can never be unopened. And that's a huge thing to do when we're so incredible raw, fragile, vulnerable, enraged, devastated and every other emotion under the sun just after Dday. Generally not the best time to make big decisions with huge consequences.
Also you said you want her to suffer. I know extremely well that feeling! I was in that place for a very long time and my feelings of wanting her to suffer were so intense I wrote my own horror movie scripts about the various almost unmentionable tortures i would inflict on her and even wished on her children so she would suffer! The rage!
Wanting someone else to suffer is not a good motivation. Wanting to help the OBS is a good motivation. You might not yet have enough information to decide if telling or not telling is the best option.
Lately I've been feeling more sorry for AP than fury at her for her incredibly delusional disrespect of another woman. I feel sorry for her because she's gotta be a mess to do something like this!!! In her case, i don't think she's evil; i think she's vulnerable, lost and hurting.
And with regard to focusing on telling OW's BS, you already have so much to deal in your own life, and likely the emotional toll this is taking on you is high, and if you're not eating or sleeping well, your energy is probably lower than normal. Better to use that energy to take care of YOU in the best way you can and put the issue of the OBS away for now, to come back to and ponder as you heal.
Another thought I had is that if the OBS already is alerted to flirty texts, then if he really wanted to know, maybe he would contact you? Maybe he's not ready to hear. I have no idea, just a thought.
Some say that focusing on AP and OBS is a way to shift your focus from your own WS and your own marriage, and it's totally normal, because our feelings toward our WS are muddled, love, hate, everything, whereas our feelings toward the AP are clear and full hatred. So it feels like if we rat her out, we will feel better. But we might not, and in the meantime, would it do any good, really any good to anyone? Only time and more information will tell. Others will fill you in on all the good reasons to tell, and there are many which come into play in different situations.
I just posted long long thoughts on this under another Just Found Out newbie under Betrayed by my Brother.
I believe very, very strongly this is not at all a black and white issue. The issues around it are not so simple, they are actually very complex. And it really is horrible to have the information, infuriating to carry a secret, and not know what is the right thing to do. So if you're not sure, wait. Focus on yourself and leave it be for now. Someday you will know what to do.
I still struggle with it whether it's better or not to tell, but I am personally very happy I didn't ask rashly when I was at the height of my agony. And every situation is different.
My very best to you as you start this journey through hell. I wish you strength, compassion for yourself, and patience, and trust that you will be okay, but it might take a bit of time to feel that. I'm definitely still working on it, but i am better.
((Hugs))