It's like giving some power over to your children rather than hoarding it all to yourself. Especially if you ask them to forgive you. So many parents think they have to appear perfect to their children but I think you're doing them a greater favor if you teach them ways to cope with being imperfect - as we all are. If you can tell them, from time to time, 'I made a mistake', you might find them willing to say the same back to you some day. Then they have learned to take responsibility for their behavior.
Excerpt from Buddhism for Mothers: A calm approach to caring for yourself and your children. I found this selection listed in SouleMama's Book List, and then checked it out from the library. I've found it to be so helpful! Also, I checked out: Calm and Compassionate Children, a handbook by Susan Usha Dermond. These are both great & will be, I'm sure, added to our home library in due time.