NO

Lots of responses to this one so I try and discuss them here. Firstly my question was not whether the Sioux WOULD have used such a weapon but would they have been justified to do so? Although it is ironic that many of you invest more morals in a people that (at that point in time) the US did not even class as human. If as most say no, even when faced with the destruction of your nation and population then when would it be justified? If the answer is still never then why have them? Secondly I used the question of nukes to take the question of "collateral damage" to the extreme. If it wrong to drop a nuke then what about a cluster bomb or cruise missile? How many innocent civilians deaths constitute an immoral act? When you kill 70 people it is murder, when you kill 100,000 or more it becomes a statistic. Before we get on our moral high pedestals on this, lets remember that we live in a democracy. Even if we did not vote for the button pushers, we support the system that put them there and as such are morally culpable.

No they would not destroy that much

Part 1 of the question is hard enough for me, I have always said I will not go and fight in another country as I do not believe all my government tells me, and the people there may well see me as an invader as I would see any armed force moving into my country. If a nation is preparing to attack would I launch a pre-emptive strike thus saving my people - hmmm, maybe.
Part 2 I can only answer with, as justified as any other nation in the same circumstances.

they love the land

It is doubtful that the Sioux would consider ever developing using such a weapon. I think they woule be offended to be used in such a question using then in a European (white man's) hypothetical morals question like that.

The development of the atom bomb in America was done because the Germans were also working on its development. The Germans surrendered 3 months before the atom bomb drop on Hiroshima. On a population of mostly civilians who new nothing of atomic weapons. The scientists that worked on the bomb celebrated the success, the science worked, later many of those who worked on the project questioned its use and suffered as a result, empathy is a powerful thing, is it right to kill thousands of innocent people, the young the old. Is it "moral" to blow up a school full of people because you don't like one of the teachers? Death on these scales and for these reasons can never be "moral" I encourage anyone who thinks it is to listen to Carl Sagan reading the pale blue dot.

First, the U.S.'s genocide against Native Americans was wrong, unjust, and evil. If Native Americans had an organized military that could have opposed the U.S. then things would have gone much much different. They would have been justified in defending themselves against an invading army.

But responding with a nuclear weapon that would likely have killed more than a million civilians is just as evil. Using atomic weapons should never be an option. Not even a last option. Such weapons can't be used simply to eliminate military targets. They kill innocent people and leave behind destruction and radiation that will bring suffering to many more in years and even decades to come.

War should be the last resort after all other options have been exhausted. When the U.S. bombed Japan during WWII around 150,000 to 200,000 people were killed. We could have demonstrated the power we had by dropping a bomb on a smaller target or even a nearby island but our government chose to kill innocent people instead.

So, to answer your question... SHOULD the Sioux (Native Americans) have used atomic weapons against New York and Washington? I'd say absolutely not. If they had nuclear weapons then they would have had other options as well, including diplomacy.

What killed most in those days was a biological weapon like flu and colds inadvertently of course. That would be an ethics questions. Knowing several different kinds of people from different tribes I would say the majority would refuse just on the grounds it would be contamination of the Earth.