@DangerMouse33 I’m really sorry you’re in this position, it sounds utterly heartbreaking. From what you’ve said, this wasn’t a violent or sexual incident, and no one was hurt. It was a moment of poor judgement, he touched her shoulders and told her off in company, and he’s apologised. You’ve acknowledged he was wrong. That’s all anyone can reasonably expect.
But there is a lot of info missing from your post, i.e the ages of the adult children and whether they live at home with you or you all live together in his or your home. I think that could make a big difference. So I am writing this on the assumption the DC do not live with you.
Adult children absolutely have the right to set boundaries, but they don’t get to dictate your entire romantic life unless the partner is abusive or dangerous. What you’ve described doesn’t fall into that category. How would they feel of they brought a partner to see you and you didn't like the way they acted adn you told them it was you or you go NC?
Going NC over this, and the second DC threatening NC unless you leave your partner, feels disproportionate and emotionally loaded.
You don’t need to choose between them. You can hold your line calmly: “I love you, I’m here when you’re ready, but I’m not ending my relationship over this.” Then leave the door open. They may need time to cool off, and that’s fine, but you don’t have to dismantle your life to satisfy an ultimatum.
Sometimes adult children do overreact, especially when there are complicated feelings about a parent’s partner. You’ve been with your DP for years; it’s okay to protect that relationship while still loving your DC. You’ve already shown you can be honest about DP’s mistake. Now the ball is in their court.
Hold steady. Don’t chase. Don’t grovel. Let them sit with their feelings. They may well come back once the dust settles.