
This is from what I remember... In the first timeline, the emperor died right? Then the war between Linden and Mil regarding the succession of throne started, and eventually Linden won..
After Linden won, he killed Mil's relative and those who are on his side, and I think Elise is one of those who were close with him (though I know that this is only one of the reasons, since the narration said that she had done more evil things but it was not stated)
I hope I'm remembering it right It's been awhile since I've started reading this..

Yeah she just wanted attention and because of that, she became a villainess in first timeline. ╮( ̄▽ ̄)╭
Her family is more on Lindens side I think. It would be stupid of them if they loved their daughter to support Mil, when their daughter was married to Linden. It would have been like killing her and I do not think they wanted that. Even with her selfishness in first timeline.
But I do not have a better explanation for the prince's actions either. So lets say he just hated her and justified him wanting to get rid of her with the harassments the servants had to bear from her and executed her for that. But maybe previous commenter was right, I do not know anymore.( ̄∇ ̄")
Guys, my I know why ML kill Elise in the first timeline?