They weren't an "army" army. They were a bunch of friends and newly added allies, who had army-like qualities, but didn't have anywhere near a strict hierarchy as you describe. They never signed any contracts saying they had a serv, never agreed that they couldn't argue with the leader.
Call them an army, a mob, or a herd, it doesn't matter. But that "bunch of friends" had been following Buffy for 7 years, and she had been leading them quite well. In an endeavor that literally involved life and death decisions on a daily, if not hourly, basis, she had pulled them through with only one major injury, Xander's left eye. That is a truly phenomenal record. I believe that such a record should earn her a degree of faith and support.
As for the Potentials not being an army, never signing a contract, and never agreeing not to argue with the leader, no, they never raised their hands and took any kind of oath of fealty to Buffy or her cause, any more than she raised her hand and swore any sort of oath to patrol the hellmouth and fight the things that go bump in the night. By being the Slayer, and by being the Potentials, cruel as it might sound, volunteering was never an option. They were drafted. Until the moment when Buffy gave all of those girls the choice as to whether they wanted to become Slayers, as cruel as it might seem, free will never entered into the equation. And even if that weren't the case, by the simple act of seeking and receiving Buffy's support and protection, whether willingly or out of self preservation, the Potentials, by being under her protection, also fell under her authority. Her house, her rules. Quite simple.
And, as I said before, they DID have the option of walking out the door any time that the rules became too harsh or the risk became too great for them. Unfortunately, the risk was far, far greater on the other side of that door than it was, all safe and snug, there inside. And it wasn't that they didn't accept the fact that they had to have a leader, their objection was that they didn't want a leader who expected and required them to take a small portion of the exact same risk that she had been taking on their behalf ever since they arrived in Sunnydale. Then, lo and behold, their new leader proceeded to almost immediately lead them out on a mission that proved to be even more of a disaster than the battle at the vineyard had been. And, of course, they had no choice but to oust her just like they did Buffy. Okay, she was laid up in bed, barely able to walk, so there might have been some logic there, or at least there would have been if they had then elected Giles, Willow, or Xander as their new leader. They were, after all, not just the obvious choices, they were the ONLY choices left.
So why, instead of doing that, did they decide to accept Buffy as their leader once more? Could it have possibly been that, at last, the Potentials and the Scoobies gotten some small inkling of what being the leader involves, and none of them wanted any part of it? Could it possibly have been that, with the undeniable evidence of the Scythe in her possession, they finally had to accept the fact that Buffy had, after all, been right all along about the vineyard and its importance? (Just as she was right all along about trusting and believing in Spike, but that is only valid here by way of pointing out that Buffy was good enough at her job, after been doing it for seven years, to assess the facts and, when necessary, trust her instincts to make the hard decisions, and to make them accurately)
Let me say once more, I am most certainly not trying to say that Buffy didn't make her share of mistakes in this situation. She did. Mistakes were made all around. And the Scoobies were totally within their rights to make their doubts known concerning Buffy's plan. Their choice was wrong, but they were entitled to make it. What they had absolutely no right to do, however, even Dawn, was to throw Buffy out of her own home, or to even suggest that she leave. If they didn't like what was required of them there, they should have left. I can pretty much forgive, or at least accept, all the rest. But not that.