Well, the Catholic position avoids all dilemmas like that. We simply believe that she was given the fullness of grace at her conception, and not at three, or two and a half, or one second before the Archangel descended.
This being said, when a child disobeys, it does not constitute sin. The Church teaches that the age of reason begins at 7 at the earliest; anything prior to that is not a wilful disobedience but mere instinctive behavior which cannot be sinful. It is a case of invincible ignorance -- another case of people free from all sin, contrary to the literalist reading of "all have sinned" in the Romans.
For the record, the Orthodox position does not say that the Theotokos was zapped by God with grace at age 3 without regard to her will (as is self-evidently the case in the Catholic dogma.)
She arrived at a state of theosis at the time of the Entrance as a result of a process of synergia between her will, choices, and actions and the action of God's will and grace. That state of theosis grew and intensified as her life went on.
Even from that point, she was fully capable of sinning or choosing other than the will of God. I seem to recall something in the services of Annunciation or in the writings of the Fathers that poetically says that the dead in Hades, the angels, and indeed all of creation waited in awe and silence waiting to hear how the Theotokos would respond to the message of the Archangel Gabriel. Would she assent and say that she wished this conception to proceed according to the will of God?
Age 7 at the earliest? I sincerely hope you keep this a closely guarded secret in your youth Sunday Schools. :) So, actual sin isn't possible until the age of reason? "Honor thy father and thy mother" means nothing until the age of reason? I have no problem with the idea of them not being held accountable on the same level as us in terms of salvation, but I've never heard of this blank check idea before for children that old. All this prompts me to ask how you define the age of reason?
BTW, I love invincible ignorance! Let's face it, my only shot at heaven is that I am LOADED with it. :)