Question: How can I get my kids to submit to my authority the way God intended?
Answer: The best way is to model what you tell them to do, tell them in a firm but loving way, and as they are able to understand, tell them why it is important to obey what you are telling them.
It is important for us to know why God’s laws are what they are (they are always designed for our greatest good) and it is important for our kids to understand why they are doing our laws, otherwise they do not become an internal ethic that drives their decisions throughout life, but merely a standard they do not understand or appreciate.
Of course, if your kids do not submit they must face logical and reasonable consequences for their disobedience. These should range from less to more severe depending on the attitude or severity of disobedience. A couple of great books that might help in this process are Loving Obedience: Child Training Techniques that Work, by William Richardson, and Parenting Adolescents, by Kevin Huggins (my favorite parenting book of all time).