C172 flight instructor reported after landing with a rough running engine; they did not follow taxi instructions which resulted in a taxiway incursion.

Narrative

I was instructing a student the morning of Day 0. After we completed our maneuvers we were heading back to ZZZ when we started to have a rough running engine. We ran our flow and checklist and suspected a possible mag issue and/or possible carb ice. We informed ZZZ Tower of our rough running engine and that we wanted a full stop. We did not declare an emergency because we were still making sufficient power. We decided to stay higher than normal in case we lost our engine and therefore made a steep descent to land. We were able to land safely under power on Runway XXR as we were cleared. Upon landing we were instructed to exit Runway XXR on taxiway 1 if able; then a pause but the same transmission; taxi straight in to the ramp the firetrucks will follow you on the ramp. I read back 1 straight in to the ramp. We turned off the runway on 1 and kept it rolling because of the rough running engine. We did not see any other aircraft on the taxiways then we turned on taxiway 2 to taxi to the ramp via taxiway 3 like we thought we were cleared and would normally taxi. Tower did not say anything about the deviation or give us a phone number to call nor did they tell us to switch to Ground as I assumed they were getting us out of the way. After we got on the ramp by the firetrucks; I monitored Tower and Ground to see if the trucks were going to try and talk to us. I did not change to Ground earlier because Tower never told me to switch. We taxied back to the hangar safely and did not talk to the fire department. The taxi clearance we normally receive is taxiway 2 to the ramp. The firetrucks were located near taxiway 3 on the ramp in our normal route. Our engine was still running a little rough causing the plane to vibrate more than normal during the taxi. The higher workload of the situation caused me to misunderstand what Tower told me to do because of our expected instructions and 1 and 2 both having the same word in them. I must have been thinking taxiway 2 to the ramp; like we always get; because of the higher workload and stress. The firetrucks were positioned where we always turn off of 2 so I must have thought that I was turning there because they were going to follow us and that is the taxi instruction we always receive. Also because of the higher workload and expected taxi route; I might have confused the meaning of straight in because taxiway 3; which we always exit on; comes straight out of the ramp at a 180 degree angle which in my head meant that we just go straight into the ramp from it; and taxiway 1 is at a 45 degree angle; which in my mind at the time; does not go straight into the ramp. After the flight; I briefly talked to our flight club president on the phone and chief flight instructor in person about the rough running engine and I left the airport as I had no more flights scheduled. Once I was home; the president and chief instructor text me about debriefing from the flight. In order for me to review everything that happened; I went to the recording to listen to the ATC recordings. After listening to the recordings; I realized that I did not follow Tower's instruction to taxi to the ramp via 1 instead of 2. Once I realized this; I filled out this report. I think that the stress caused from the increased workload from the rough running engine caused me to confuse ATC's instructions with a taxi clearance we normally get; especially because the taxiways have similar names. Luckily no other planes were around and no one was harmed. I have learned a lot from this experience and I hope that others can as well.