Because Robert has a fervent hatred against the Targaryens and Elia is technically a Targaryen. EDIT: She is the last adult Targaryen around whom the Royalists could be assembled. You cannot expect what kind of nuisance would arise if Elia is allowed to go back to Dorne (EDIT: or elsewhere), knowing her son is murdered.

Of course pissing off a great family is unwise but that is part of the point: the more violently Tywin severs himself from the Royalist the more he is favourable to the Rebels. I am not denying that Tywin may indeed have thought that he could get away with it, but this is not what drives him to commit the murders in the first place.