Interesting question. Words in English often evolve over time such that the words get used in less specific situations. Then, if that newly-coined usage becomes widespread enough, that meaning will eventually make its way into dictionaries also, as the dictionaries catch up with the vernacular.
When I look up the word divorce on Wordnik, for example, the first definition I see matches the one you gave:
divorce (n.) The legal dissolution of a marriage.
However, the second definition listed is one that would indicate that A and B could also be "divorced" from an affair, particularly if the affair had been lasting for some time:
divorce (n.) A complete or radical severance of closely connected things.
Other, more-general definitions from Wordnik include:
- separation; disunion of things closely united.
- part; cease or break association with
As for bitter turns, you've committed a cardinal sin on ELL by not telling us where you found this quote, so I'd have to speculate a little bit. But, generally speaking, if something like a breakup takes a "bitter turn," we can assume that it didn't go as smoothly as expected.