Pilot reported an engine malfunction required an immediate landing at a nearby airport; however the tower controller denied the pilots pattern entry request and was uncooperative even though the pilot was experiencing an engine malfunction.

Narrative

I experienced an engine that started to shake along with a burning rubber smell and some visible smoke from the prop spinner area. Immediately I turned towards ZZZ airport and called the Tower. I [requested priority handling]; stated my position as 15 miles west of the airport; inbound to land. The Tower Controller told me to enter a right base for XXR. I said that I wanted to preserve my altitude and just go directly to the airport; then circle down from there in case I lost complete power. I knew at my altitude; I would enter the Bravo airspace and requested that she give me a Bravo clearance; again stating that I'm [requesting priority handling]. I was aware that I could use my [priority] authority to enter the Bravo without a clearance; but I still had the time and distance to receive a Bravo clearance. Tower said no; they can't give me a Bravo clearance and again instructed me to enter a right base for XXR. Frustrated that they didn't seem to understand the situation; I called ZZZ1 Approach on XXX.X; [requested priority handling] with them; got the Bravo clearance; he even read me the current ATIS; then once I was overhead ZZZ; they switched me back to Tower. I reduced power to idle and made a normal power off 180 landing; and was able to taxi to parking on my own power. I'm very disappointed in how ZZZ Tower was not helpful in my situation. Even on a normal day; that controller seems overwhelmed and stressed out; spacing airplanes on 5+ mile finals; yelling at planes to widen the base leg to abnormal sizes; then when I experienced my [problem]; gives me instructions contrary to what I felt was the safest course of action and unhelpful overall. Honestly; I feel that ZZZ would be a safer airport with no control tower (class E) than the service that I received.