my favourite anecdote about singers who didn't get along is about these guys - Sam and Dave... this is by far their most famous track.
they broke up in the early 70s due to differing views and ambitions about their career, like so many other acts. they worked 'together' through studios a few times afterwards, but it wasn't until a particular bass player tricked them into being in the studio
at the same time a few years later that they lived up to their heyday.
and the result:
aww yeah