Sounds like a good place to start! All you have to do is say, "Insert name, I'm sorry for my bad behavior around your children, I am working hard to make sure that doesn't ever happen again." And that's it, you're done, it's out of your control at that point. Whatever happens, happens but at least you put your big girl pants on and apologized. Don't expect warm fuzzies or a hug or forgiveness, just do it and get your side of the street clean. The chips will fall as they fall and you will live through it!