Skyhawk 172/Cutlass 172
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Flight Crew Last 90 Days 39.1; Flight Crew Total 400; Flight Crew Type 200
Situational Awareness; Confusion; Communication Breakdown; Training / Qualification
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Airport; Procedure
My student and I were returning into the pattern for a few laps in the pattern. We were instructed to report over the VOR. At that point it was around XA:45 we were told to continue straight in for a stop and go and make left closed traffic. The pattern at that point got really busy. On downwind we were told to make a right 360 and re-enter downwind: we did. Then we were told to extend and look for a Skyhawk over the VOR we were number 4 to land and that we would be turning in front of a Seminole 5 miles past the VOR. We spotted a plane with lights just crossing the VOR; but we could only count 2 planes on final my student was on the comms the whole time and did a great job inquiring if we were number 4 and that we were following the plane over the VOR.The tower confirmed that so we started turning inbound on an extended left base as that plane crossed the VOR. I then noticed a plane about a mile past the VOR on final and told my student to re-enter downwind. We allowed that Skyhawk to pass however we were confused because that Skyhawk wasn't over the VOR and originally I confused it for the Seminole. The Tower controller then yelled at us for starting to cut in front of our traffic and we apologized. We asked for a touch and go but she cleared us to land at that point. We continued on to land and she asked us to get off at B1; however; there was a plane holding short of runway 4 at B1 so I told my student to continue to B2 and expedite. She then realized there was a plane there and asked us to get off at B2. She never gave us taxi instructions so after we were clear of the runway we jumped in to get clearance as soon as we could but a plane had already landed.After we secured the aircraft we came in to find out tower had called to apologize for taking out as she said 'her mess' on us. Just thought I'd submit a safety report as it was a very hectic and confusing transition in.
A busy traffic pattern and mis-identification of pattern traffic resulted in evasive action for the C172 instructor and student pilot and a few moments of concern and cutting and pasting of traffic by the local controller at LYH.