"...the rocket's red glare; the bombs bursting in air..."

Bit unfair to take that as an indication of a national American tendency towards violence. Those are British rockets and bombs, being used against Americans.

Pedantic point: the United Kingdom in not a federation - otherwise there would be a separate English Parliament and government, which there isn't. True enough, if Scotland voted for independence they'd get it without any hassles (probably) - things have moved on a bit since Ireland voted for independence after the Great War. On the other hand, I think it likely that, if Texas wanted to leave the Union, it would have the same kind of problems it had the last time it wanted to do that.

It seems to me that, if America is more publicly violent in some ways, that could be a reflection of a kind of populism which is related to democracy. The death penalty is a case in point. Most civilised countries look askance at America's love affair with it, but if they put it to the vote in England it'd probably get voted for by a majority, and that'd apply in a lot of places. (Not everywhere - when there was a referendum on whether to have the death penalty outlawed in the Irish Constitution, there was a clear vote in favour of doing precisely that.)

The popularity of violent films, and so forth, indicates that the rest of us are pretty obsessed with that kind of thing. But having the violence take place in America, or in other fantasy countries such as China, perhaps helps keep it a fantasy separate from reality.

I've never heard that domestic violence is any worse in America than in other countries. I think that would be the key indicator.