So, the killer was (spoilers)

At the end of Psycho II we are led to believe that Miss. Spool was Norman's real mother. But in Psycho III this turned out not to be the case. She was actually his aunt, but part of her delusion was believing that Norman was her own son. It was revealed in Psycho III that Miss. Spool had kidnapped Norman when he was a baby and murdered Norman's father (who Miss. Spool had been in love with). The corpse that Norman kept in the original Psycho was Norman's true mother.

Dear old Aunty Emma turned out to be MORE insane than either Norma or Norman!!

Norman blacks out when he kills, and Norma, when she was alive, didn't kill anyone. But Aunty Emma killed knowingly, anyone who stood between her and the son she wanted for herself. She's the nuttiest one of all!

I think the killers were Lila and her daughter