The commander of the base wrote, “I do not presume to understand current politics, but what I do know is the concerns of the US administration discussed by Vice-President Vance on Friday are not reflective of Pituffik Space Base.” in an email and was thus dismissed. In dismissing her, the Pentagon stated this reason. “Actions [that] undermine the chain of command or to subvert President [Donald] Trump’s agenda will not be tolerated at the Department of Defense.”
No, second in command is the Secretary of Defense. But if the Vice President is acting on behalf or under direction of the president it could be seen as a billet. Walking around bases every unit has pictures of their chains of command, all of them include the VP and have for a long time.