OP, I have a different perspective to share. I view you as a strong woman trying her hardest to heal a broken family.
Everyone's feelings and perspectives should be heard and addressed in family counseling, to include your own.
I found this Atlantic article insightful - separate realities explained. We all have different perspectives of events, conversations, etc...
https://www.theatlantic.com/family/archive/2019/02/my-adult-daughter-doesnt-speak-me-anymore/582361/
You've got two daughters with differing perspectives, your own perspective and your husband's as well. What he did, as you describe, was not a good behavior. He likely lied to/gaslighted DD as he was terrified and acted on a coward impulse. And while a major breach of trust, it was one action on one day that must be taken into consideration in terms of the whole of his actions and behaviors. He completely devastated her idea of who he was as a Dad. He has caused perhaps irreparable harm to her in terms of trusting men, as her role model in a pivotal time of her adolescence. He needs to own this and they will both need time to heal together on their own for many years.
I can empathize with you as my Dad had an affair that blew up in a nuclear manner - caused the entire family great pain to include severe career repercussions, local social shunning issues (we might as well of all had the plague) and a very public disgrace - all of his kids generally hated him for many years.
However, he redeemed himself over time with all his positive actions and behaviors, was not a serial cheater, and is the best Dad ever. He's been remarried for 20+ years to a different woman (not the AP). So in my case, my Mom and Dad didn't work out.
What was so difficult at the time everything went public was realizing my Dad wasn't perfect, he was a liar, a cheat, and living a hypocrisy. With time, he became human, and I realized that me not understanding parents aren't super-humans at a young age was hard to digest. I grew up fast over a few years.
I learned to forgive the older I got and once I realized I wasn't a super-human wife nor parent either, I began to see him via a new perspective.
It's worth fighting for your marriage and family through therapy. You aren't a carpet for not wanting to throw the towel in. You are the inverse - someone strong capable of seeing someone you love make a huge mistake and giving them the opportunity to right the ship.
No matter how this works out for you, I view your original post as a Mom who cares very deeply about her entire family and is devastated. You will survive, and your kids will too. It will take time and therapy. Hugs.