There is a difference between having control and building up. Parental authority based on control leads to manipulation, domination, and failed relationships.
Parental authority that is based on building up takes time, requires dependence on God's power and leads to lasting, deepening relationships.
Paul in 2 Corinthians 13:10 says that God gave him authority for building up and not for tearing down. This is important. As a parent you want to do far more than simply control your children.
Control can be achieved in many ways. Here are just a few examples:
Manipulation. Do what I ask and you can have a special dessert or your can go to the big game next week.
Intimidation. "Do what I want if you know what is good for you."
Emotional ploys. "It hurts me so much to see you argue, please stop so we can have peace."
Power plays. "I am your parent, I am in control. You answer to me."
Threats. "If you don't come right now, no videos for a week."
Anger. "If you would behave, I wouldn't get angry."
Building up is achieved by actively engaging in the spiritual battle for the souls of your children. You understand that your authority is given to you by God so that in every situation you can point your children to the wonder of Christ.