The purpose Belinda wanted to get rid of Serenity was because Serenity was the eldest daughter-in-law of the York family. As long as Serenity was alive, the Yorks were backing the Hunt sisters, and they would join forces with the Stone Family to deal with the Fisher Family.
Belinda sacrificed family ties to ascend to the position she held today. After several decades in this position, she could not simply hand it over to the descendants of her elder sister.
Back then, she was cruel enough to e