there is a big difference in having countries come together in a union and a unified country breaking apart into sub-units.

True enough, and it wouldn't be easy - but it's a reality that Czechoslovakia (and earlier Denmark) managed to negotiate amicably enough, and one which the United Kingdom will probably have to deal with once again soon enough (having screwed up the first time round in relation to Ireland).

It doesn't have to mean any kind of hostility or loss of a very close relationship.