I imagine that if the pro-slavers had had the majority, and attempted to impose slavery throughout the Union, it would have been the anti-slavery people who'd have wanted to secede.

I've never been at all clear what the constitutional situation is regarding secession - is it that there are no circumstances under which a state can secede from the union, and that this was laid down in the constitution? Or was it just that the southern states didn't go through the proper procedure?

So far as I am aware, in all the discussions about the European Union at present, it seems pretty generally agreed that if in the future a country wishes to secede, it will have every right to do so, even though it might be extremely inconvenient.