INSTRUCTOR PLT WITH SPI ON NIGHT TRAINING FLT IS REQUIRED TO FILE IFR TO LAND AT DEST ARPT. THERE IS A HDG DEV AND ACFT IS ON A COLLISION COURSE WITH A B737. CTLR INTERVENES.

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IT STARTED 15 MI NE OF HPN. AS I APCHED THE ARPT IT BECAME APPARENT THAT I WOULD NOT BE ABLE TO LAND VFR. WHEN I WAS DIRECTLY OVER THE ARPT AT 1500 FT MSL; I ADVISED THE TWR CTLR THAT THE ARPT WAS NOT IN SIGHT AND THAT I SHOULD CONTACT NY APCH TO 'PICK UP' AN IFR CLRNC. THEY ADVISED ME TO FLY A HDG OF 270 DEGS; WHICH I PROCEEDED TO DO. I CONTACTED NY APCH ON 120.55; I BELIEVE; AND TOLD THEM THAT I NEEDED THE ILS RWY 16 FOR HPN. THEY ASKED ME IF I WAS IFR EQUIPPED AND ABLE; AND I RESPONDED AFFIRMATIVE TO BOTH QUESTIONS. NY APCH ADVISED ME TO FLY A HDG OF 320 DEGS. I TURNED THE ACFT TO THE ASSIGNED HDG OF 320 DEGS. I THEN BEGAN TO SET UP MY APCH; TUNING AND IDENTING THE ILS AND OM; THE CARMEL VOR FOR MY MISSED APCH; AND REVIEWED MY CHART FOR THE APCH. THIS IS WHERE THE PROB AROSE: WHILE FLYING ON MY 320 DEG ASSIGNED HDG; IT WAS APPARENT THAT I WAS ON A DIRECT HDG FOR A B737 ON THE ILS RWY 16 HPN. AT THAT TIME IT WAS APPARENT THAT THERE WAS PLENTY OF SEPARATION SO I DECIDED TO WAIT INSTEAD OF QUESTIONING ATC. AS I CONTINUED MY FLT PATH IT WAS APPARENT THAT THIS WAS GOING TO BE A CONFLICT. JUST SECONDS BEFORE I WAS GOING TO QUESTION ATC; THE APCH CTLR CAME ON THE FREQ AND ADVISED ME TO TURN L IMMEDIATELY. I BEGAN TO TURN TO THE L AS HE ASKED WHEN HE CAME ON AGAIN AND ADVISED ME THAT I WAS HDG DIRECTLY AT A B737 ON THE ILS. AT THAT POINT I WAS ALREADY IN MY TURN TO L. AFTER HE EXPLAINED WHY I WAS TURNING L AND WHY HE NEEDED ME TO TURN L; HE ASKED ME WHAT HDG I WAS FLYING. I IMMEDIATELY ADVISED THE APCH CTLR THAT I WAS ON A HDG OF 325 DEGS. I ALSO HEARD THE B737 JET BEING REVECTORED FOR THE ILS BECAUSE I IMAGINE HIS TCASII MADE HIM BREAK OFF THE APCH AND GO MISSED. I KNOW MY HDG WAS 325 DEGS BECAUSE I NOTED MY HDG WHEN HE TOLD ME TO TURN L IMMEDIATELY. I CONFIRMED MY HDG WITH THE HDG INDICATOR; MAGNETIC COMPASS; AND VFR AND LORAN. THE LORAN ACTUALLY READ 323 DEGS AT THAT TIME. AFTER BEING REVECTORED FOR THE APCH I WAS GIVEN A HDG OF 110 DEGS TO INTERCEPT THE FINAL APCH COURSE AND APCH CLRED ME FOR THE ILS RWY 16 HPN. AFTER 2 MINS OR SO; I REALIZED 110 DEGS WOULD NOT INTERCEPT THE FINAL APCH BECAUSE I TURNED 10 DEGS TO THE L AND THE NEEDLE STARTED TO COME ALIVE. WHEN I MADE MY OWN CORRECTION ANGLE; ATC ADVISED ME TO TURN 10 DEGS L TO GET A BETTER ANGLE; WHICH I ALREADY HAD DONE BY THEN. THE ILS WAS UNEVENTFUL AND THE PLANE WAS LANDED WITHOUT FURTHER OCCURRENCE. THINGS THAT COULD HAVE AFFECTED MY PERFORMANCE: THE FLT WAS A NIGHT TRAINING FLT WITH A STUDENT PLT BEING PREPPED FOR HIS PVT PLT CHK RIDE. SO I WAS IN THE R SEAT WHICH COULD AFFECT MY VIEW ON THE INSTS. IT COULD CAUSE ME TO FLY A HDG OF PLUS OR MINUS 5 DEGS I AM SURE. ALSO I THOUGHT IT WOULD BE A GOOD IDEA TO EXPLAIN WHAT I WAS DOING TO THE STUDENT SO MY ATTN WAS A BIT AVERTED TO THAT. ALSO I WAS ON A DOWNWIND RADAR VECTOR FOR AN UNEXPECTED ILS ARR SO COCKPIT WORKLOAD WAS HIGH AT THAT TIME. THINGS I SHOULD HAVE DONE: BEEN MORE AUTHORITATIVE AND QUESTIONED ATC EARLIER OF A SIT OF CONFLICT. IT DEFINITELY COULD HAVE BEEN AVOIDED IF I HAD ACTED MORE AUTHORITATIVE.