Help finding specific story

Hey this might be a shot in the dark but I’m looking for one of those female reincarnation stories.

The one I’m thinking of is the female lead goes back in time and has to rebuild her relationship with the ML and son. However the only thing I can solidly remember is there’s a story at the end that shows an alternate path where the FL didn’t come back and it shows the son who didn’t grow out of being completely apathetic to everything, goes to war/battle (?) and just dies because he didn’t really have anything to live for (It’s like a winter scene).

I just read https://www.mangago.me/read-manga/the_flower_dance_and_the_wind_song/ which I thought was the same story but had a different ending