There's plenty of reasons not to divorce, Money is one, reputation is another, social dynamics is one (perhaps a divorce would make 2 families become enemies.), there are lots of reasons to not divorce despite lack of love. In fact, marrying for love is a rather recent phenomenon, plenty of people throughout history had mistresses, lovers, concubines, or visited prostitutes despite being married. Marriage was more a political and social tool for much of history, so I had no doubt that sexual relations outside of marriage was widespread.
Granted this story is just a fetishization of NTR or cheating, so it doesn't deserve that much thought I think.