As I walk honestly before God, with my children watching, they will learn how to have a real relationship with him as well. As they see me apologize to them and pray in front of them to ask for God's forgiveness in my own life, my children will learn that God is a God of grace who forgives me and guides me. My worshiping him in gratitude for a beautiful sunset or a rainbow gives them a pattern for their own spontaneous worship.
As my children see me in the deep waters of life, being tested to my core and still holding on to my 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.