Though we as Christians live in a democracy where liberty of the individual is a priority doesn't mean that we are not under authority. Christianity can be best applied in a democracy as we have the liberty to choose what is best for us as Christians who live a disciplined life. We have the freedom to choose God and live by His commandments. Thus, we are in the world but not of it ~ 2 COR 10:3. That means though we have God given free will to make our own choices, we give that over to our Creator and pray always His will be done. For it is His will that is truly the best for us. Yet, that giving over has to be our choice.
Our children have to do the same. And, they will with/in the knowledge of parents unconditional love which is given to them even prior to their birth. As God loved Jesus and us (He is in us/we in Him) before the creation of the world ~ John 17:24, 1 Peter 1:20; so, too we know our children and we love them unconditionally. It is that kind of love that we discipline them with and in. In this love, they will make the choice to obey as they know first hand of that love and in that love their very life depends on and from it they will have enjoy long life because of it.
"Children obey your parents in the Lord, for this is right. Honor your father and mother which is the first commandment with a promise that it must go well with you and that you may enjoy long life on the earth" ~ Ephesians 6:1.
How to discipline then? Love them, and show them that you too are under a higher authority - The Word of God given to us by the Creator of Heaven and Earth of all things seen and unseen ~ our Lord and Savior Jesus Christ who is God!
This also applies to adult children. We come under parents authority. We must still honor thy father and mother as adults no matter how old we are as children. This respect shows our respect love for God. In this way, we all are children of God.