When you say “the power” do you mean the physical ability, or the moral right?
Let's start with the moral right and go from there, we can move the former later.
Does a parent have the moral right to give orders, make decisions, and enforce obedience among their children?
Does you boss have the moral right to give orders, make decisions, and enforce obedience at your place of employment?
The parent accepts the responsibility for protecting the child from their own lack of mature judgement. This is like asking “do I have the right to push a drunk guy off the train tracks when the train is coming”. It’s a judgement call; you are put in a position to have to guess at what the person would want, and guessing they want to be saved from a clear and present danger is reasonable enough. The decision is rooted in defense of that individual, not in violating their right to free movement by pushing them; not in having authority to enforce obeying your will. A grey area, but the core principle is defense of
their rights, not exercising your own perceived authority.
So no, the parent does not have authority, nor does the train hero. They are simply trying to defend the self-authority of the other person, as to sit back and watch them kill themselves would be contrary to what they would presumably choose, and here’s the key - they are not in a position to make a rational decision decision about it for themselves at that time.
Your boss does not have authority over YOU, he has “authority” (property rights) over his property - the business. I can tell you “don’t sit on my couch” but that is not authority over you personally. It’s rooted in my right to decide how my property is used.