tl;dr The captain is in charge, but he is incapacitated, so leadership is a bit in shambles.
As far as depicted in the show, the captain would have absolute authority and you'd have a person worthy of command in charge. Such a person was actually in charge, this was captain Radic, but he was poisoned by Dr. Smith early in season 1. He is replaced by captain Kamal who obviously still struggles with absolute command in crisis situations.
Aside from the captain you have a few leaders also, most importantly:
- Victor Dhar: leader of the colonists. While a leadership position, in effect he still is there only for the single journey, this would make his authority lower than the permanent crew of the Resolute.
- Hastings: Intelligence officer, but during the show more 'head of security'. He clearly has loose morals and does not hesistate to blackmail/threaten people to get what he wants.
- Ben Adler: Director of advanced systems, basically in charge of scarecrow, important position.
And then of course there are the Robinsons, who despite not officially being in charge, constantly try to manipulate other people to follow their lead (of course, since they're the heroes, that would be the correct action ;)).
So you have an absolute chain of command, but because the top is still getting used to her power, these other authority figures have it easier to get their way, and it evolves more into a power-grab between them.
For the scene you are talking about, Hastings was initially convincing captain Kamal to abandon the stranded people because they did not have enough resources for the journey home. She (i.e. the captain) agreed to this.