I got the impression it was because she was quite young and couldn't handle all the responsibilities that came with the marriage. She agreed to a divorce and giving up her child because she thought that was the right thing to do. She seemed to regret both.
In the Anime on netflix, it was due to the husband's mother & fam who looked down on hazuki (big sis) just bcause she doesnt really know how to cook do house chores etc. While the Husband is indeed a very nice person and someone she loves dearly, they ended up having an argument which led to the divorce. Surprisingly, it was nice to see her still having a nice relationship with the ex-husband. I mean she was barely 17 when they got married, the mental torture from the in-laws mustve deeply exhaust her
Was it ever explained why the older sister got divorced??