Without trying to sound like one of THOSE guys. Edelgard is a rather complex character as several people above have said.
She's villainous, emotionally cold, and bullheaded about her goal are the aspects one could describe her... if you plays the other routes.
According to my mild research, outside of her route, only two other routes show her as a somewhat sympathetic villain at her end where the last other route outright shows her as absolute evil.
Regarding Edelgard herself.
As far as I'm concerned, she's a well-meaning person who simply chose a path that she had no choice in taking. Her path was forcibly laid out in front of her by her past and the scheming conspiracy hidden beneath it. If Sothis was capable of rewinding even further back before the game's start, I believe an alternate route would be possible that leads to her happiness proper without the bloodstained path being present, but alas, Sothis isn't that almighty. However I am glad that Edelgard is the character they chose for this role.