A C172 CFI ALLOWS HIS PVT INST CANDIDATE PLT TO FLY OFF RWY HEADING DURING A MISSED APCH AT DAY; OH.

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THE PLANNED LESSON WAS A LONG XCOUNTRY FOR THE INST RATING. THE WX AT DEP ARPT AND ENRTE WAS FOGGY WITH OBSCURED SKY; VV100 FT; WITH THE WX CLRING BY TKOF TIME TO MARGINAL VMC CONDITIONS. JUST BEFORE TKOF AN UPDATED WX BRIEFING GAVE A FORECAST OF 500 FT BROKEN 2 MI VISIBILITY AT DAYTON AT OUR ETA. I WAS THRILLED WITH THE FACT THAT THE STUDENT WOULD GET TO EXPERIENCE AT LEAST 1 APCH; AN ILS; TO ABOVE MINIMUMS ON THIS TRIP. THE FIRST ARPT WE MADE AN APCH INTO WAS ALMOST CAVU WHEN WE ARRIVED FOR THE APCH. ENRTE; ON THE SECOND LEG TO DAYTON; ATIS SHOWED THAT THE WX NEVER REALLY CLRED AND WAS HOVERING AT MINIMUMS. SOME OF THE 'BIG BOYS' EVEN SUGGESTED THAT THEY GO TO CAT II APCH; AS WX WAS BORDERLINE FOR ILS. STILL THINKING THE EXPERIENCE WOULD BE GOOD FOR THE STUDENT; I PLANNED TO CONTINUE WITH THE APCH; MISS AND CONTINUE TO OUR ALTERNATE; WHICH HAD VMC CONDITIONS. SIMULTANEOUS ILS WAS IN EFFECT ON PARALLEL RWYS; SO I EMPHASIZED THE IMPORTANCE ON THE APCH OF NOT DRIFTING TO THE R OF LOC. ON THE ILS APCH; WE WERE ASKED TO KEEP OUR SPD UP FOR FOLLOWING TFC. WE ENTERED THE CLOUDS ABOUT 600 FT ABOVE DECISION HT. THE STUDENT DID A FAIRLY GOOD JOB ON STAYING ON THE LOC AND STAYED SLIGHTLY ABOVE GLIDE PATH AS I SUGGESTED SEEING WE WERE FOLLOWING AN ACR ON THE APCH. AS WE GOT NEAR DECISION HT; THE STUDENT WENT R OF THE LOC. I TOLD HIM TO CORRECT; BUT SINCE WE WERE CLOSE TO DECISION HT; I WAS ALSO FOCUSING ON ALT AND LOOKING FOR RWY ENVIRONMENT. AT DECISION HT; THE GND STARTED TO APPEAR; BUT NOT RWY ENVIRONMENT; SO I CALLED FOR MISS. THE STUDENT; WAS BUSY WATCHING FOR RWY; AND CALLED RWY IN SIGHT ON OUR L. I TOLD HIM TO FLY THE MISS; RWY HEADING. SEEING THE STUDENT WAS ALLOWING THE ACFT TO TURN R AND DIDN'T SEEM TO BE NOTICING IT OR MAKING A CORRECTION; I GOT ON THE CTLS. BY THE TIME I STOPPED THE TURN AND STARTED TURNING TO THE RWY HEADING; WE WERE QUESTIONED AS TO OUR HEADING; WHICH THE STUDENT RPTED AS 270 DEGS; 30 DEGS FROM RWY HEADING. WE WERE THEN GIVEN A VECTOR FOR OUR MISS. AT THE STUDENT'S REQUEST; WE TRIED ONE MORE ILS. THE NEXT APCH RESULTED IN SPOTTING RWY AT MINIMUMS AND LNDG. TAXIING TO THE FBO; GND CTLR 'BUSTED OUR CHOPS' ABOUT OUR MANEUVER ON THE MISS. KNOWING THAT THE APCH WAS LIKELY TO END IN A MISS; I SHOULD HAVE EMPHASIZED THE MISSED PROC MORE WITH THE STUDENT BEFORE THE APCH; INSTEAD OF CALLING IT OUT WHILE EXECUTING THE MISS. ALSO; I SHOULD HAVE BEEN 'ON THE CTLS' MORE; KNOWING IT WAS THE STUDENT'S FIRST TIME TO MINIMUMS AND NOT KNOWING HOW HE'D HANDLE THE SIT FOR REAL. (HE WAS WATCHING THE 'VIEW' OUTSIDE THE ACFT AFTER DECISION HT INSTEAD OF FLYING THE ACFT.)