score:7
Not exactly an affair, but Borte, Genghis Khan's first wife, was abducted by a rival tribe. Genghis Khan didn't care and took her back. Chagatai on the other hand kept accusing his elder brother Jochi of not being his father's son because of this, but nobody paid much heed to it.
Why... I guess Mongols just didn't care all that much since their leader was decided by election anyway.
Upvote:3
There were rumors of an affair between Marie-Antoinette and Fersen (https://en.wikipedia.org/wiki/Marie_Antoinette). The French Wikipedia entry even suggests that Marie-Antoinette had affairs with women (https://fr.wikipedia.org/wiki/Marie-Antoinette_d%27Autriche).
There were also rumors of an affair between Cardinal Mazarin and Anne of Austria, some are even suggesting that Louis XIV was the son of Mazarin and not Louis XIII. (https://en.wikipedia.org/wiki/Cardinal_Mazarin).
But these are just rumors, though they have been around for more than two centuries.
Upvote:9
Caroline of Brunswick who was consort to George IV had many affairs (although technically most of them were before she became Queen consort). While her husband ended up hating her, she was popular enough with the people that she suffered only the gossip and disdain of the court.