What a whirlwind OP! It does sound like you're considering staying, and instead of telling you what you should or shouldn't do, I just want to leave you with some questions to consider.
Will he be willing to do an STD test?
Would he be willing to do couples counselling? And take the steps to set this up, plus be open in it?
Has he truly apologised for how he's treated you, re making you feel like you're the problem?
Has he recognised it's problematic to have involved his kids in this by sending videos of them? That he disrespected you as a mother as well as a wife?
Is he still going to work with her?
Has he told anyone else in your social circle?
Has he broke things off with her or blocked her?
Have you seen messages to confirm this? Do they leave things open to reconcile?
Is he willing to have an open device policy until trust is rebuilt?
Could they be messaging on work apps, and is there a way he can build trust on this?
Is he facing professional repercussions?
Is he willing for you to contact her? (If you want too.)
If you did split, what would ideal custody look like for him?
Is he willing to divide financial assets to make it easier for you to leave if you decide too?
Is he willing to take accountability for his actions by telling family, should you want him too?
Has he been honest about how this came to fruition, and continued? How has he justified the time and energy he's poured into her instead of your family?
Has he considered divorce, and why hasn't he filed instead of continuing an EA?