PA28-161 ACFT ON TRAINING FLT AND FLYING IN IFR WAS BEING VECTORED BY APCH CTLR WHEN AN ACR ACFT UNEXPECTEDLY EXECUTED A MISSED APCH. APCH CTLR CONTINUED VECTORING RPTR; BUT RPTR FAILED TO MAINTAIN ASSIGNED HDG.

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IT BEGAN AS A FINAL CHK FOR A STUDENT PRIOR TO THE PVT CHKRIDE. THE STUDENT AND I PRACTICED THROUGH MANEUVERS FOR ABOUT 1 HR THEN FLEW TO ANOTHER ARPT TO PICK UP A CYLINDER FOR THE FLT SCHOOL. AS WE WERE FLYING TO VRB; WE DID NOT KNOW OF A FAST MOVING LINE OF TSTMS HDG IN OUR DIRECTION. AFTER DEPARTING VRB; THE WX WAS DETERIORATING FAST. I DECIDED TO FILE IFR BACK HOME. THE PROB AROSE WHEN A COMMERCIAL AIRLINER WENT MISSED APCH UNEXPECTEDLY. THE APCH CTLR; WITH A NERVOUS TONE; TOLD ME TO TURN R 090 DEGS BECAUSE OF THE AIRLINER GOING MISSED APCH AND ASKED ME IF I WANTED TO STILL TRY THE ILS. I SAID YES; WHILE TURNING TO THE R. FOR SOME REASON I DRIFTED BACK TO A HDG OF 360 DEGS WHILE MY ATTN WAS DIVERTED TO THE APCH I WAS ABOUT TO DO. THE APCH CTLR LATER TOLD ME TO RESUME FLYING A HDG OF 360 DEGS AND I REPLIED WITH 'ROGER.' I DO NOT BELIEVE THE CTLR WAS PAYING VERY MUCH ATTN TO ME RATHER TO THE AIRLINER WHO HAD TO HOLD. THE CTLR ALSO STATED THE AIRLINER WAS 'NO FACTOR.' I BELIEVE THE STRESS OF KNOWING THE AIRLINER HAD TO GO MISSED APCH DIVERTED THE ATTN OF ME AND THE CTLR.