C172 PLT FOLLOWED THE WRONG TFC POINTED OUT BY ATC AT AZO; TWICE.

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I WAS RETURNING FROM THE SW WITH MY WIFE (A STUDENT PLT) WHO WAS TALKING AND COMMUNICATING WITH ATC AS I FLEW AND WATCHED FOR TFC; WHICH WAS HVY AT THAT TIME. ATC VECTORED US TO A HDG OF 310 DEGS AND ADVISED US OF OTHER TFC NEAR US AND SOMEONE OVERTAKING US FROM THE R. A FEW MINS LATER WE WERE CLRED AS #3 FOR THE R BASE FOR RWY 17 AND THE TFC WE WERE FOLLOWING WAS AT OUR 12 O'CLOCK POS AND 2 MI. WE SPOTTED WHAT WE THOUGHT TO BE THE TFC AND STARTED IN A NE DIRECTION. ABOUT 15 SECONDS LATER; ATC QUERIED OUR DIRECTION. WE TOLD HER NE AND SHE RESPONDED THAT WE WERE SUPPOSED TO BE ON 310 DEG HDG AND MAKE AN IMMEDIATE TURN TO 270 DEGS AND FOLLOW THAT TFC. WE SPOTTED A PLANE HDG N WITH NO OTHER VISIBLE TFC AND RESPONDED 'TFC IN SIGHT.' WE WERE THEN INSTRUCTED TO MAKE AN IMMEDIATE EMER CLB AND THE TFC WE WERE FOLLOWING WAS NOT THE PLANE ATC WANTED US TO FOLLOW. WE WERE THEN INSTRUCTED TO FLY HDG 090 DEGS AND CONTACT TWR. WE DID; AND WERE TOLD TO LAND 230 DEGS; NOT 170 DEGS. THERE WAS A LOT OF CONFUSION ON THE RADIOS. ATC WAS ISSUING A LOT OF CLRNCS VERY RAPIDLY. SOME PEOPLE WOULD NOT RESPOND. ATC WAS GETTING STEPPED ON AND THE GND LIGHTS AND STROBES OF THE CITY AT DUSK MADE IDENTING TARGETS VERY DIFFICULT. I THINK THE EXTRA WORKLOAD ON ATC ALLOWED THIS SIT TO DEVELOP AS WELL AS THE CONFUSION CREATED IN THE AIR. WE WERE HAVING A DIFFICULT TIME GETTING A BREAK ON THE RADIO TO QUESTION ATC. ADDITIONAL CTLR AND RADIO FREQ COULD HAVE REDUCED THIS CONFUSION AND POTENTIAL PROB.