I managed to partially answer my own question regarding the right of revolution and the civil war. I found the following article:
Bullets and Ballots: Lincoln and the "Right of Revolution"
Author(s): Thomas J. Pressly
Source: The American Historical Review, Vol. 67, No. 3 (Apr., 1962), pp. 647-662
Reading the article, I noticed a few things:
1. Some confederates did appeal to a "right of revolution" but not all of them. I'd be curious to know how it was discussed among confederates.
2. In the article, there is no mention of "right of revolution" being linked to the second amendment. It seems supporters of such right went back to the Declaration of Independence for their justification.
3. The Union did not seem to ever entertain the idea that the confederates had a "right of revolution". Did the Union act unconstitutionally? (I'm sure some people in the South would argue that it is the case.) If the Union did not act unconstitutionally, then what is the legal argument as to why the "right of revolution" did not apply to the confederates?
4. Lincoln struggled with the idea of "right of revolution." Before becoming president he did applaud revolutions in other countries. At the same time, he spoke against taking up arms in a democracy. He himself was called a revolutionary by his opponents when he was campaigning but he denied the charge and kept insisting that the correct way to effect change was through the democratic institutions. When the civil war came, he had to clarify his position because some confederates appealed to this right of revolution. Here is what Lincoln said:
The right of revolution, is never a legal right. The very term implies the breaking, and not the abiding by, organic law. At most, it is but a moral right, when exercised for a morally justifiable cause. When exercised without such a cause revolution is no right, but simply a wicked exercise of physical power.
When he says "never a legal right", he implies that the constitution does not recognize that right because any right recognized by the constitution is by definition a legal right. I find myself in agreement with Lincoln. The moral right is not the same as a constitutional right. Heck, just about every week I find myself having to point out to someone that what is legal is not necessarily ethical and what is ethical is not necessarily legal.
As to the "right of revolution" in the NH constitution or the constitution of any other state, I see such rights being there for rhetorical effect as a reminder that the government will be forcibly deposed by the populace if it makes their life unbearable. If and when the revolution does come, there will be one of two outcomes:
1. The revolutionaries fail. The right of revolution won't save them. I can't see the day when a state court is going to say "oh, yes this violence you inflicted upon the government and your fellow citizens is alright because you have a right of revolution."
2. They succeed. In which case they won't go to court, which as part of the newly deposed government was corrupt anyway, to ask whether what they did was right. No, no. As good revolutionaries, they are going to declare their own actions to be right. Which is what all good revolutionaries do. It would be strange indeed for revolutionaries who win the fight to say "Oops! Sorry. We did not have a good reason for our revolution."