I have to hand it to you. Kudos for working on this with your children.
Parenting is a challenging job. I've taken in foster children from homes where parents gave up and gave up their children. The children were devastated, likely permanently so.
Your family togetherness means the world to them, even through challenges.
I agree with "rainyday," I wouldn't be too harsh on myself.
It sounds like the family unit is processing the family meltdown moment well.
You sound like a responsible parent. You'll take more steps if there are more which should be taken. Otherwise, it sounds like this event was handled well, with helpful/healing follow-up.

WC