If Michael had not failed completely, the Sanders might have given him a little more time.
It was precisely because he had failed that all their schemes failed, and the Sanders started to lose their patience.
The Sanders also knew that the descendant of the Duncans was powerful enough to threaten their interests, and that power was led by the Swans.
The Swans were now in control of the Harken's economy. Even after the Sanders had done so many shady things in the dark to destabilize the Swans' economic status, it was to no avail. In fact, it made them look like clowns, so they could only choose to take the risk.
The best way was to make use of Jeanne's relationship with Edward.
Once her identity as the daughter of the Sanders was revealed to the public, Edward and she would become complete enemies. In other words, Edward had to kill her.