I would submit it is not coercive to have dominion over your own house. That one's children are in effect "Trapped" under your care is a function of reality. For example If I take someone up in a hot air balloon that I own. I have every right to remove them from my property if they do not follow my rules. However, I may not throw them out of my balloon 1000meters in the air, that would be murder. The physical reality is your children's upbringing is that same hot air balloon. You must safely ferry them to a place where releasing them from your property would not kill them. You are not "Coercing" them to stay on your property (and thus abiding by your rules) you are preventing their demise at the hands of the physical reality of the world. 

On the Broader point, government is a mental game we play with each other. We all pretend that we are, in some ethereal way in the same "group" as everyone in our geographical vicinity. That is not a physical reality. That is simply something people like to do. Other people do not like to play that mental game. It is only when the mental game of "I'm the boss and you have to do what I say" meets the physical reality of extortion(taxes), kidnapping(arrests), and murder(the death penalty) that this game becomes not so fun. And to invoke the metaphysical as some sort of justification for the behavior of those not participating in an illusory mental game is a bit myopic. God is my ruler not because of some vote, appointment or some other contrivance. God rules because God created the physical reality I dwell within and the rules of reality itself. The words of men are simply inconsequential to the will of God because it physically can't be any other way.