Please, I'm begging you, could you stop treating me like a dog or cat?

Literal

Please-I-beg-you dog-cat treatment doing [object-の] stopping receive-[could-you-もらえますか]?

お願いですから ('I'm begging you, please') is an intensified plea. 犬猫扱い ('dog-cat treatment') means 'treating someone like an animal' — dismissive, subhuman handling. やめて貰えますか is a polite request using ~てもらえますか ('could I receive the favor of your stopping'). The mix of desperate pleading (お願いですから) with grammatically polite request form creates pathos.