"Ear doctor's" vs "Ear doctor"

In the possessive construct, the possession has been elided: the ear doctor's is short for the ear doctor's office. You see this with respect to people's homes, too -- "I'm going over to Bob's", for example.

The Stephen King quote is ambiguous because we also talk about going "to the doctor", but in US English we don't talk about going "to Bob" in that case. (I have heard that construct in Israeli English, for what that's worth.) "We went back to the ear doctor" would have been correct there; that focuses on the person while the possessive focuses it on the office. Perhaps Mr. King had unpleasant memories associated with the place more than the person and thus chose to focus on the place.

The first instance is an implied object, for example

we went back to the ear doctor's [clinic]

we went back to the ear doctor's [office]

we went back to the ear doctor's [place]

The second refers to the person of the ear doctor or is a metaphor for the experience of the visit or treatment, although it's hard to tell from the quotation.

The [visit to the] ear doctor once again produced the smell of alcohol

[Dr. Johnson] once again produced the smell of alcohol