C172 STUDENT AND INSTRUCTOR RECEIVE RELAYED CLRNC FROM ATC TO ABANDON THEIR APCH WHILE SHOOTING A CIRCUITOUS LDA/DME ARRIVAL AND APCH TO NON-TOWERED VDZ.

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MY STUDENT AND I WERE ON A COMMERCIAL TRAINING XCOUNTRY FLT TO VALDEZ PIONEER FIELD (VDZ) IN VALDEZ; AK. AT APPROX 1 HR 10 MINS INTO OUR IFR FLT PLAN; WE RPTED OUR POS AT 11000 FT MSL; 10 MI N OF PEPPI (THE IAF) AS INSTRUCTED; AND WERE CLRED BY ZAN FOR THE LDA/DME-H APCH INTO VDZ. AT THIS POINT; WE WERE INSTRUCTED TO RESUME OWN NAV; TO SWITCH TO THE LCL ADVISORY 122.9 CTAF FREQ; AND TO RPT BACK TO ATC AFTER EXECUTING THE PUBLISHED MISSED APCH PROC. VISIBILITY AND SKY CONDITIONS WERE MIXED IMC/VMC. WE BEGAN THE APCH BY TURNING NE TO CAPTURE AND FLY THE 40 DME ARC OFF THE 259 DEG RADIAL FROM JOH VOR AND BEGAN TO DSND TO 8000 FT MSL. AS WE NEARED THE NEXT FIX AT KUCET (AT 319 DEG RADIAL OFF OF JOH) TOWARD THE FINAL PORTION OF THE ARC; MY STUDENT NOTED THAT WE WERE INSIDE THE ARC AT ABOUT DME 37.5 AND TURNED THE ACFT ABOUT 30 DEGS TO THE L TO A NORTHERLY HDG TO RE-INTERCEPT THE ARC; WHICH HE ACCOMPLISHED JUST PRIOR TO PASSING OVER KUCET. AT KUCET; HE BEGAN THE TURN TO A HDG OF 119 DEGS TO CAPTURE THE NEXT INTERMEDIATE SEGMENT BTWN KUCET AND LOC TO INTERCEPT AT INEYO AND DSNDED TO 7800 FT. AT THIS POINT; WE WERE APPROX 25 NM W OF VDZ. AS WE BECAME ESTABLISHED ON THIS INTERMEDIATE APCH SEGMENT; WE RECEIVED A CALL FROM AN AIRLINE FLT INDICATING TO CONTACT ZAN. WE CONTACTED ATC IMMEDIATELY AND WERE INSTRUCTED TO TERMINATE THE APCH; TURN TO A HDG OF 090 DEGS; AND CLB TO 9000 FT. WE COMPLIED WITH THESE INSTRUCTIONS AND ASKED ATC WHAT THE PROB WAS. (MY INITIAL THOUGHT WAS TFC AVOIDANCE.) AT THE TIME ATC CONTACTED US; WE HAD THE VDZ ARPT IN SIGHT. THE CEILINGS AT VDZ WERE RPTED 6000 FT BROKEN. WINDS WERE OUT OF THE W AT ABOUT 16 KTS; FAVORING A CIRCLE-TO-LAND APCH TO RWY 24. ATC EXPLAINED THAT ACCORDING TO THEIR RADAR WE APPEARED TO BE HEADING TOWARD AN UNSAFE MIA. WE EXPLAINED TO ATC THAT OUR VISUAL AND INST REFS PLACED US ON THE INTERMEDIATE SEGMENT BTWN KUCET AND INEYO ON COURSE FOR LOC INTERCEPT. WE INDICATED THAT WE HAD THE ARPT IN SIGHT. ATC THEN CLRED US TO RESUME THE APCH AND CONTACT THEM BY PHONE AFTER LNDG AT THE CONCLUSION OF THE FLT. ONCE BACK ON THE GND; WE SPOKE WITH ZAN. THEY INDICATED THAT THEY BECAME ALARMED WHEN THEY OBSERVED OUR ACFT TURNING TO A NORTHERLY HDG AWAY FROM THE LOC DURING THE INITIAL PART OF THE APCH SHORTLY AFTER GIVING US THE APCH AND FREQ CHANGE CLRNCS. WE REVIEWED OUR FLT PATH ON THE TRACKING SYS AND DETERMINED THAT WE HAD; INDEED; DRIFTED TOO FAR INSIDE THE ARC. WE OBSERVED THE POINT WHERE WE ATTEMPTED TO RE-CAPTURE THE 40 DME ARC BY TURNING TO A NORTHERLY HDG AWAY FROM THE LOC FINAL APCH COURSE. WE APPRECIATE ATC'S OVERSIGHT AND LEARNED THAT EVEN MINOR RTE OR ALTDEVS WILL BE CAUSE FOR ALARM AND POSSIBLE ATC INTERVENTION.