Lucy, lately, wants to do everything I do. When I fold laundry, she wants to fold laundry (she takes an item out of the basket, wads it up, and carefully sets it on the bed). When I wash dishes, she wants to wash dishes. When I pray, she imitates me. She finds a little book, kneels or stands or sits, and babbles in the tone of voice I usually use for reciting the Divine Office.
It had a flash of insight the other day, as she was doing this. In the Sacrament of Baptism, the intention to "do what the Church does" is sufficient for a nonbeliever to validly perform the Sacrament. In a similar way does it not stand to reason that the prayers of a toddler "doing what Mommy does" would be acceptable to God?