If anybody ought to resist the temptation to muffle questions and questioners it ought to be fathers. Now that I have children I realize this truth more than ever. I can never truly silence either the question or the questioner; I can only cause the question not to be asked of me. If I silence the questioner they always have mom, maw maw and paw paw (my wife's parents), grandma and poppy (my parents) and the list of uncles and aunt continues on from there. The truth is, the older they get the more options they have: teachers, friends...
Since children are by nature questioners, I owe it to myself to engage the process. If they are asking questions I want to be part of the expedition searching for the treasured answers. The greatest damage we can cause to our children is to become angry at their questions. There is safety in verbalized questions. The only questions that you need to fear from your children are the ones they don't ask. You can only shape their views if you provide a venue for them to verbalize their internal struggles.
I refuse to raise children that are afraid to ask questions about: the existence of God, the inspiration of scripture, standards and anything else that questions them. Even if I don't know the answer I will take the journey with them to find it. Your children either are, or will, struggle with these issues. Make sure you are the one they are asking the question to. I can say this without fear as I have periodically struggled deeply with these issues. Faith that has never wrestled with the fundamental question of God maybe pure, but it is also immature.
Never avoid questions because you don't know the answer. Never be afraid to admit that you do not know the answer. Better to say that you don't know, than to give a bad answer. We must be willing to work through the questions with our children. I know that I have only been a parent for a couple years, but I have been a son for 36.
Ultimately, what you do with questions is wrestle with them until you get the answers. You should never muffle them. You should also never weary of the same question. Some questions are too important for you to quickly answer them; they must be wrestled with and prayed over.
Two Books I recommend:
The Sacredness of Questioning Everything, David Dark
Heaven: The Heart's Deepest Longing, Peter Kreeft