Regarding the spoiler
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The duke is not "framed," he actually was fully involved as a traitor...the only difference is that halfway through, the motivation for his betrayal disappeared so that he would no longer benefit. However, he was already in too deep, so he disowned his son to keep him from being involved in the rebellion.
It's still a Happy Ending, though, because the Duke is allowed to live after the rebellion (in a different country) under a false identity.
It's a sad story in general, though the ending sounds even worse when taken out of context (ie, me only talking about the Duke's ultimate fate).
If you look at the rest of his family, the ending's a bit happier (though still bittersweet).
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The FL and her son prevent the coup from happening. The son turns down a title as a reward, and went with his mom to her mother's (?) country, where they find out that the Duke wasn't executed as they were told, but banished...to the same country. So the entire family lives Happily Ever After together.
Just as you'd expect in that situation, I assume. (I haven't read any spoilers that specifically answer this question, so below is purely supposition based on stories with similar situations.)
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The Duke got neck deep in a rebellion against the royal family; only chance out of it was succeeding, which it didn't. Anyone who fails a rebellion against the king has their entire family executed (except for their very small children, since infants and toddlers are presumably not involved), and their lands and titles taken by the royal family, who usually give them out as rewards to their loyal followers.
The son probably would NOT have been given his dad's lands and titles, despite being raised to succeed them. He contributed to the royal family, but not QUITE that level. He probably only would have made Count...which doesn't really matter, since after being disowned by his father, he's now legally considered a foreign noble through his mother's family. (This has nothing to do with his dead uncle's land and titles, which I hope were handed back to his cousins post-attempted coup...I haven't heard anything about that, though.)
I haven't read the novel, but there is literally a spoiler thread on NovelUpdates.
https://forum.novelupdates.com/threads/the-flower-dance-and-the-wild-song-%EA%BD%83%EC%9D%80-%EC%B6%A4%EC%B6%94%EA%B3%A0-%EB%B0%94%EB%9E%8C%EC%9D%80-%EB%85%B8%EB%9E%98%ED%95%9C%EB%8B%A4.117872/
I just need someone to tell me that this will have a Happy Ending please ╥﹏╥