Just for clarification on this please.
Forgive me if I duplicate something already said. I frequently respond without reading responses from others to ensure that my words are not influenced by the thoughts of others.
In a literal sense, the head of the house controls everything in the house but I don't think that is what you're asking. I think that you're asking how much is the appropriate amount of control and how that control should be exercised. I can't define another man's house and family so I'll answer that using myself as the measuring stick.
Most importantly, I very rarely give demands. I have their complete devotion and dedication. They want to please me. A polite request gets the same results as a demand usually. No human is perfect so there are exceptions but this applies about 8/10 times if I were to estimate
If I instruct them to do something rather than politely request it is because they were reluctant to act on a request. This is my way of saying that I believe it to be essential but it's also their invitation to ask questions or present their explanation of why they don't want to do this thing. I hear them out and if they have good points then I give those points the proper amount of consideration. Sometimes that means I change my mind, sometimes it means I alter my request, sometimes I still believe that the original instructions must be followed. Regardless of my decision, I treat them with dignity and let them know that their thoughts were heard. This happens about 15 percent of the time and they abide my decision 99% of the time.
If I demand that they do something they don't question me or delay. They follow my instructions to the letter. Once the task is done they are given the opportunity to ask why I demanded it. Usually the answer is that it was urgent and we didn't have time to discuss it. Much less often it might be that they still refused the request. That might seem silly to ignore if they know that I will demand it next but they are human and sometimes, very rarely, are a little bit stubborn.
Normally they know what I expect of them, what they expect of each other and of themselves. They are mature adults so they fulfill those expectations and there's no need a try to control them. They are responsible with money and only exceed their daily spending limits in case of emergency. We all agreed on the spending limits and they don't act irresponsibly so again, no need for control.
I think we have a healthy relationship. We discussed what is needed of each of us, what we expect of each other and we assigned responsibilities very early in the game. We review as needed but we all strive to do our part. Because of this I only need to make requests, give instructions or make demands in our of the ordinary circumstances.