The first line of authority is the parent.
Let your children be partakers of true Christian training; let them learn of how great avail humility is with God how much the spirit of pure affection can prevail with Him how excellent and great His fear is, and how it saves all those who walk in it with a pure mind. For He is a Searcher of the thoughts and desires [of the heart]: His breath is in us; and when He pleases, He will take it away. –Clement I
Let your children be partakers of true Christian training. Ship them off to other people who know better than you. The government or the church are both good examples – just pick your poison.
Where do I get my authority to raise my children? Or even more specific, where do I get the authority to lead my children with regards to my faith in Christ? God gives us roles as fathers and men to lead our families. We are to seek Him with a pure mind and then lead our kids to Him. The mere fact that He blessed me with children is my authority.
I really want to break off the main topic here and just give thanks to God for the children He gave me. I am beyond blessed with the two He has given me. There really are no words that would sufficiently describe them in my life. Glory to God in the highest.