As we walk honestly before God, with our children watching, they learn how to have a real relationship with him as well. As they see us apologize to them and pray in front of them to ask for God's forgiveness in our own lives, our children learn that God is a God of grace.
As they see us in the deep waters of life, being tested to the core and still holding onto the Lord and choosing to believe the best, this observation will prepare them for their own trials, which will surely come. They will know that he will guide and forgive them as they lead an imperfect but devoted life before a loving Father who has always met their mother's needs.
Read more about this in The Mission of Motherhood.