She has the authority to order members of Starfleet to their death to accomplish a mission or to save her ship and crew, but Neelix is not a member of Starfleet. She has the legal right to order him off the ship, but not the legal right to demand he lay down his life.
BTW, would anyone who has seen Ashes to Ashes care to comment on the similarities or differences between the cases of Lyndsay Ballard and Tuvix?
Who would stop her from doing whatever she wanted? The only ones who could stop her, is a mutinous crew. Starfleet is 70,000 Light Years away, they have no contact with her, and no way to give her orders, until that happens, she answers to no one but herself, so she has whatever authority she assigns herself, as long as she has the muscle of the crew supporting her.
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?