A compound layering of extreme politeness markers. 申しません is the humble (kenjougo) negative of 言う 'to say.' おやめ頂きたい is an honorific request construction: honorific prefix お + masu-stem やめ + 頂く (humble 'receive') + たい 'want' = 'I would like to (humbly) receive your stopping' = 'please stop.' The sentence-final わ here is the emphatic feminine marker. The whole sentence layers multiple keigo devices into a hauteur-softened demand — a distinctly feminine high-register scold.