In the immediate, you might feel this urgent need to "win" or feel a sense of justice, so let me give you a picture 15 years out....
If they leave you for the OW, you don't win. They both got what they wanted and you get screwed.
If he stays and begs forgiveness and you try and move on from this, you get him, but you still don't "win". You get trauma you have to deal with, endless work, pain and one of the most awful experiences. Maybe if you do incredibly well, you end up with a better marriage but it's not "winning" because the cost is so high.
If you leave him with him begging and clinging to your legs, and he rejects OW and sits crying for years in his underpants while you go onto a joyful life with private jets and an amazing new husband, you still don't "win", because this happened and it will always hurt.
No one wins when someone cheats. Read that again, several times. You never "win". What you do is survive it.
In my story, he dropped OW very quickly and cried, begged, pleaded. And we endured OW harassing us while we were trying to work through things. Went on for months, made everyone ill. In the end we got the police involved and she finally got the message. Six weeks later she was "in love" with another married man.
Us?
I went through years of betrayal trauma, he got ill, the pain was engulfing and in the end we divorced after the three hardest years of my life.
He ended up sad, sick, alone and still misses us and regrets every day what he did.
She ended up (and this is not being mean it is being honest) about 25 stone, alcoholic, still alone once she ran out of married men to shag.
I got a new life and new husband, but I will never have "won". Seeing them suffer doesn't give me that, or take away the pain and losses. It was just something I had to survive.
What will make a difference to you in the long term will be what you did. You don't get to choose whether you have to deal with the cheating or not, sorry. Your agency over that was taken from you.
You do get to decide where you go from here.
I am very proud, looking back, that no matter what an abusive psycho cunt the OW was to me, that I kept my dignity and calm.
I am very proud that I was generally kind and classy about the whole thing, even though it killed me at the time.
What I regret was the desperation I felt for my husband to "pick" me as if a lying cheat was the prize. That doesn't mean I hate him because I don't. I love him and always will, but he did what he did and it was his value and not mine which were diminsished.
What makes you valuable right now is all your good characteristics, your self respect, your courage, being a Mum, being classy and not being the kind of woman who is trying to text someone else's partner with their baby there.
Try very hard to step back from what you are feeling and see that inherently makes you better than either of them.
I have worked for years in infidelity mentoring in support groups, and I absolutely promise you in almost every case this stuff happens because the two people involved are damaged, have weaknesses, flaws and fuck ups.
It doesn't happen because the affair partner is "better".
That is never the reason.