With the kids, I think it's important they have the opportunity to talk about it, and how they feel. They should still go at their own pace. I just worried tho, if you just try to keep the conversation light and avoid discussing this, they might feel like their feelings here don't count. Or like it's being brushed aside. It would probably be a good thing to let them open up if they need or want to, and that you care.

Seperately is a good idea, just acknowledge how your actions hurt them and that you are sorry. You still love them and are there for them, and just ask them if the have anything they want to say, let them know if they need to talk that you are there. They might talk or might not, but they know the door is open if and when they are ready.