A C182 PLT ALONG WITH A SAFETY PLT WERE MISIDENTED BY ATC DURING A PRACTICE MISSED APCH AT ARLINGTON; (KAWO) WA.

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THE EVENT THAT COULD HAVE COMPROMISED SAFETY OCCURRED WHILE ON A MISSED APCH FROM ARLINGTON WASHINGTON (AWO). THIS WAS THE SECOND OF 2 PRACTICE APCHS. I WAS THE SAFETY PLT. THE PF WAS WEARING FOGGELS. I WAS NOT OPERATING THE CTLS AT THE TIME BUT WAS LISTENING TO ATC AND LOOKING FOR TFC AS WELL AS GENERAL XCHKING OF THE FLT TO HELP PRECLUDE ERRORS. WE WERE CLRED FOR THE LOC APCH RWY 34 TO AWO. WE STARTED OUR MISSED APCH ABOUT A HALF MI S OF THE END OF RWY 34 AND BEGAN A CLBING L TURN TOWARD 250 DEGS AND 2000 FT. WE CHANGED FROM THE ADVISORY FREQ AT ABOUT 1000-1200 FT MSL (TERRAIN ABOUT 100-150 FT IN THIS AREA) AND CONTACTED SEATTLE APCH ON THE MISSED. WE WERE ASKED TO IDENT (WHICH WE DID). WE WERE ASKED FOR OUR INTENTIONS AND WE INDICATED THAT WE WOULD LIKE TO FLY ANOTHER LOC APCH. THE CTLR TOLD US 'THAT WAS NOT GOING TO HAPPEN' AND AGAIN ASKED FOR OUR INTENTIONS. THE TONE OF THE RESPONSE SEEMED UNUSUAL. WE THEN ASKED TO RETURN TO HARVEY (S43). THE CTLR TOLD US THAT HE WOULD TURN US S WHEN WE WERE IDENTED. HE RPTED RADAR CONTACT 2 S OF HARVEY FOLLOWED BY A CLB TO 5000 FT. WE ACKNOWLEDGED THE RADAR CLB INSTRUCTION BUT NOT THE RADAR CONTACT. THIS WAS AN INCORRECT POS RPT. THE CTLR WAS WORKING ANOTHER ACFT INTO HARVEY; SO WE DID NOT IMMEDIATELY CORRECT THE WRONG POS RPT. OUR ACTUAL POS AT THAT TIME WAS ABOUT 1 MI SW OF THE APCH END OF RWY 34. I THOUGHT TO MYSELF THAT THE CTLR MEANT TO SAY ARLINGTON AND IF HE IS USING THE ARPT CTR; WE COULD BE 2 MI FROM IT. WE CONTINUED OUR CLB ON A HEADING OF 250 DEGS. MOMENTS LATER THE CTLR ASKED US TO CONFIRM OUR L TURN. WE RESPONDED NEGATIVE AND THAT WE WERE CONTINUING 250 DEGS AS CLRED. THE CTLR APPEARED FRUSTRATED BUT DID NOT IMMEDIATELY REPEAT WHAT HE WANTED US TO DO AND WE WERE RELUCTANT TO TURN WITHOUT HAVING RECEIVED INSTRUCTIONS TO DO SO AND WERE NOT SURE WHAT TO TURN TO EVEN IF WE DID. THERE WAS NO VISUAL INDICATION OF TFC NEARBY. EVENTUALLY WE WERE GIVEN A 100 DEG HDG WHICH WE IMMEDIATELY COMPLIED WITH. THE CTLR TOLD US THAT WE WOULD MAKE A PHONE CALL WHEN ON THE GND. WE WERE THEN CLRED TO THE PAE VOR TO HOLD AS PUBLISHED. WE IMMEDIATELY TURNED TO PAE VOR AND CONTINUED OUR CLB. WE FLEW S OVER THE VOR AND PROCEEDED TO ENTER THE HOLD PATTERN PUBLISHED ON THE VOR-B APCH PLATE. ON THE OUTBOUND 329 DEG LEG WE WERE CLRED TO 4000 FT AND LATER GIVEN VECTORS TOWARD HARVEY FIELD. THEN CLRED TO 3000 FT AND TOLD THAT WE WOULD BE CLRED FOR THE VISUAL APCH WHEN WE HAD THE FIELD IN SIGHT. WE RPTED THAT WE HAD THE FIELD VISUALLY; AND WERE CLRED FOR THE VISUAL APCH. THE PF ASKED ME TO TAKE OVER AND I FLEW THE VISUAL APCH. WE CHANGED TO HARVEY FREQ AND DSNDED S ALONG THE MIDDLE OF THE VALLEY AND JOINED A 45 DEGS FOR R TFC RWY 14. ON THE GND WE PULLED OFF THE TXWY ON TO THE GND AND SHUT DOWN THE ACFT TO CLOSE OUR IFR FLT PLAN THROUGH THE CLRNC NUMBER. WE THEN TAXIED TO THE HANGAR AND CALLED ATC AS REQUESTED. IN DISCUSSING THE EVENTS WITH MY PARTNER; NEITHER ONE OF US HEARD INSTRUCTIONS TO TURN L. 1) WE DID NOT HEAR THE CLRNC TO TURN. 2) THE CTLR USED THE WRONG CALL SIGN AND WE DID NOT RECOGNIZE THAT THE INSTRUCTIONS WERE MEANT FOR US. 3) OR POSSIBLY THE XMISSION WAS BLOCKED BY ANOTHER ACFT. 4) IT IS ALSO POSSIBLE THAT WHAT I THOUGHT WAS 'RADAR CONTACT 2 S OF HARVEY' WAS REALLY 'RADAR CONTACT TURN S TO HARVEY.' IF SO IT WOULD EXPLAIN WHY THE CTLR THOUGHT WE SHOULD TURN L AND WHY WE DID NOT RESPOND. 5) PERHAPS ANOTHER ACFT IDENTED AT THE TIME WE WERE ASKED TO IDENT AND THAT IS WHY WE WERE IDENTED AS 2 S OF HARVEY. IF THIS WAS THE CASE THERE MAY HAVE BEEN CONFUSION BTWN 2 ACFT IN DIFFERENT POS. 6) THE CONTINUED CLB TO 5000 FT ON THE 250 DEG HDG DID NOT MAKE A LOT OF SENSE BECAUSE IT WOULD HAVE TAKEN US INTO THE APCH TFC AT PAE. THIS WAS RECOGNIZED AT THE TIME; BUT THE CTLR CAUGHT THE MISSED TURN PRIOR TO QUESTIONING. THE ACTUAL LOCATION WAS NOT OUT OF THE ORDINARY AS SHOWN ON THE GPS TRACKS. 7) ANOTHER FACTOR WAS THAT THERE WAS A LOT OF IFR TFC DUE TO THE PROHIBITION OF VFR OPS INSIDE THE LATERAL LIMITS OFCLASS B AIRSPACE. THE FACT THAT WE WERE HELD ON THE GND FOR ABOUT 1 HR SHOULD HAVE BEEN A CLUE THAT SATURDAY AFTERNOON WAS NOT A GOOD TIME TO DO PRACTICE APCHS.