"I'm gonna steal their kids first" isn't any better. Do need a good plan, and not one that's just repeating the same evil.
As for unquestioning obedience, yeah, it's there. It's obedience to the scariest group out there, which is the Quetz. Brand-as-Saida can be scary, but Saida isn't a massive half-deity Quetz, so it works like this.
"I'm an X, you obey Xes, you must obey me!" got met with..
"I'm going to ask your mother first, the Quetz I actually do obey without question, as you are asking me to go directly against my orders from her."
So Brand has no leverage. Not the scariest Quetz, and authority from being a Quetz is entirely devolved from Saida's mother. So no personal authourity from being scary, and no positional authourity from being a princess. Saida's mom is both scarier and higher in rank than Saida is.
This sort of thing would have worked if Brand knows how it works. But Brand has ethics and is not familiar with this kind of obedience to authourity. So Brand doesn't know how to use it.. or abuse it.
Take the example of the Captain of Köpenick, where a raw outsider can come to a place and make them do incredibly stupid things, simply due to their willingness to follow orders, and the appropriate uniform. (Body, in this case.) But Voight still knew the language, the phrasing, and enough of the culture to know how to use the privileges of the rank he didn't have. Brand doesn't know how to issue orders like this, doesn't know the language, and doesn't want to have a host of minions.
The part about talking to Saida is partially correct. A discussion with Saida about how to give the right orders, and how to stop the child-stealing, could well have worked, as Saida may well know how to give orders to Aves that will be followed out, no questions asked.
As a hypothetical, Brand could have said that too many of their children had been stolen and they need to recover from their drafts for a few seasons, and then asked a few follow-up questions. After the mayor answers them, he could have moved onto issuing more complete orders about hiding the eggs, producing a more plausible story and couching the orders in a way that makes them seem like they come from the Quetz. That could have worked, which would have ended the child-stealing for a cycle. It would have required some long conversations with the mayor, and likely some advice from Saida, but it could have been done.
Alternatively, being the big scary monster could have worked as well, but I think it would have been harder. Saida is only perhaps a bit more powerful than the average Quetz soldier, so it would have taken more prep work in my opinion. It would have taken more than fifteen seconds of flying around casting lightning bolts, though.