Found out my husband is cheating on me *update*

Backstory.. been married ten years, have 2 children (boy and girl) we both work. Im a chemist, he's a lawyer.

How I found out.. we decided to get a hedgehog for our daughter.. so I took to our local Craigslist page and found someone with a pair of hedgehogs (handled frequently, litter box trained, comes with all the bells and whistles to care for them) I had him type in the number on his phone.. and a contact in his phone popped up for the number... A woman answered "hi John, how have you been!" And when she heard my voice she was very confused.. as my husband sat across from me sweating like a dog.

I made an arrangement to meet with the mystery woman.. my husband reluctantly agreed to drive his vehicle (as it has GPS) I begin to plug in the address and it pops up in his "frequently visted" file on his GPS.. and I just say.. "how queer is that..." We get there.. my husband looks like a ghost as the woman opens the door.. and I immediately and reminded of a younger version of myself as she greets us.. and as she shifted her gaze to my husband, it looked as if she had been hit by a ton of bricks when she sees his face... Shit got super awkward.

She invites us into her home as I take lead my husband staggers behind like a dog who just got caught with it's tail between it's legs and if I had eyes in the back of my head I'd be certain that they were exchanging quizzical glares with one another as we walked into her home.. I buy the hedgehogs.. we go home.. and later on she calls him (her number now miraculously deleted from his contacts) and she gives him an earful before he can get to somewhere more private to conduct this conversation.. I hear him whispering and then he comes back and throws his phone facedown on the counter.. and I ask in a dumbfounded tone "who was that honey?" And he lies and says it's a client 😂

I redial the last caller and then she answers and gives me an earful meant for him.. and I tell her to calm down.. and joke with her that I'd be pissed too if I knew my fuck buddy was married.. she then takes my information down and has been emailing me all the texts they had exchanged over the last 6 months, receipts, ect. From their rendezvous over that time.. and now this is where I'm kinda stuck...

Do I fuck his life up royally? Do I go out with my head held high and keep it peaceful for my kids sake.. or do I just acknowledge it and make an appointment for my husband and I to see a marriage counselor?..

-----UPDATE-----

1. The woman he cheated on me with sent the screen shot of all the texts, there's not a lot in them, no pictures exchanged, nothing sexual in nature, and no exchanges of feelings towards one another.. and she mostly initiates the conversations and they mutually set up a date to meet.

2. In the messages they arranged to meet up 5 times over the six months and she emailed me telling me in those encounters that she and him had sexual contact 3 of those times.

3. In those 5 dates, they paid for their meals separately.

4. In the 3 times they had sex he insisted to use protection each time, and then he'd leave immediately after

In her last email to me she goes on to state how she felt totally used by him and how she put in all these efforts to get him more interested in her but that each time they'd meet up hed just kind of ignore her feelings and wouldn't open up to her and that the sex felt like more of a transaction between them than a genuine emotional bond.. which I can't help but to laugh about because, I don't care.. I'm not here to mend her broken heart 🤷