You're right: "...in the order in which it was received" is precisely what it should be. The phrase as it is, "in the order it was received," is grammatically the same as saying "in the manner it was done." Both phrases require an "in."

There are two options for inserting the "in" into the phrase as it stands. Because most English learners are taught to avoid ending a sentence with a preposition, "in the order it was received in" sounds incorrect, although it is technically correct. Thus, the only grammatically correct option that remains is "in the order it which it was received."

(Note: I am American, so I am abiding by the American English rule of placing commas and periods inside quotation marks--a rule I dislike, I might add.)