Wow, the sister is an asshole.
"I have a lover in university, I leave them, and my sister, to make merry in a foreign country, meet some stud there and decide to marry him"
Talk about being selfish and insensitive.
We don't know at all that's what happened lol. For all we know they most likely already broke up by the time she was getting ready to go overseas. Also, there's literally nothing wrong with wanting to find better opportunities for herself abroad in that scenario (the sister already more or less started becoming more independent, partially to avoid her incestuous feelings growing any stronger). The cheating/abandonment scenario doesn't feel right at all. There's like no signs showing Kiku was hurt or manipulated, if anything she's on very friendly terms with the older sister. So yeah, the breakup seems to be mutual.