SMA PERFORMS MISSED APCH IN IMC BUT IS DISORIENTED AND HAS LOSS OF ACFT CTL. FAILS TO TURN AS INSTRUCTED; HAS CLOSE PROX WITH SECOND ACFT.

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IT WAS BROUGHT TO MY ATTN THAT WE WERE INVOLVED IN A NEAR MISS WITH ANOTHER AIRPLANE. I WAS IN THE R SEAT ACTING AS INSTRUCTOR/OBSERVER. THE PLT FLYING THE PLANE AT THE TIME DID NOT MEET INSURANCE REQUIREMENTS TO FLY SOLO. WE WERE ON THE ILS RWY 4 APCH AT AMARILLO. WE DSNDED FROM VFR ON TOP INTO THE CLOUDS AND BEGAN THE APCH. THE APCH TURNED SLOPPY RIGHT AWAY. WE WERE ABOVE GS AND WANDERING ON AND OFF THE LOC. I WAS TALKING TO THE PLT THE WHOLE TIME TRYING TO HELP HIM STABILIZE THE APCH. HE WAS MAKING LARGE CORRECTIONS TRYING TO GET BACK ON COURSE. I NOTICED AT ONE TIME OUR HDG AND INBOUND COURSE HAD ABOUT A 30 DEG DISCREPANCY. WE ALSO HAD FULL FLAPS TRYING TO GET DOWN TO THE GS. AT DECISION HEIGHT WE INITIATED MISSED APCH. BECAUSE OF OUR AIRPLANE ATTITUDE AND CONFIGN IT WAS DIFFICULT TRANSITIONING TO MISSED APCH. AT THIS POINT THE PLT WAS DISORIENTED AND CONFUSED. THE CTLR TOLD US TO TURN TO A HDG OF 270 DEGS. I ACKNOWLEDGED; BUT WE WERE VERY BUSY TRYING TO GET THE AIRPLANE BACK UNDER CTL. I NOTICED WE WERE IN A BANK AND THE AIRSPD WAS VERY SLOW. THE STALL WARNING WAS GOING ON AND OFF. WE WERE ALSO HAVING A HARD TIME GETTING A POSITIVE RATE OF CLB. THE PLT AND I WERE BUSY TRYING TO TAKE CARE OF THE AIRPLANE; CLEANING IT UP AND GETTING A POSITIVE RATE OF CLB AND A SAFE AIRSPD. THE CTLR AGAIN SAID TO TURN TO 270 DEGS. HE THEN SAID IMMEDIATELY WITH NERVOUSNESS IN HIS VOICE. I HEARD THE CTLR TALK TO THE OTHER PLANE; AND THE PLT OF THE OTHER PLANE SAID HE HAD US ON TCASII. AFTER SEVERAL SECONDS OF FIGHTING THE PLANE (I WOULD GUESS NO MORE THAN 20-30 SECONDS); WE WERE BACK UNDER CTL AND ON OUR ASSIGNED HDG. THE CTLR NEVER ADVISED US OF A PROB. HE THEN PROCEEDED TO GIVE US VECTORS FOR ANOTHER APCH. WE NEVER SAW THE OTHER AIRPLANE OR EVEN KNEW WE CAME CLOSE TO IT. I REALIZE THAT THE APCH WAS BAD FROM THE BEGINNING. WE SHOULD HAVE SCRAPPED IT; AND STARTED OVER BEFORE IT GOT OUT OF HAND. THE PLT WAS TRYING TO SALVAGE THE APCH BY MAKING LARGE CORRECTIONS. WE ALSO SHOULD NOT HAVE DUMPED IN THE FLAPS AND DOVE FOR THE GS. NO MORE THAN 15 DEGS SHOULD EVER BE NECESSARY. I; AS AN INSTRUCTOR; SHOULD HAVE TAKEN OVER THE AIRPLANE BEFORE WE GOT INTO TROUBLE. THE WX SURPRISED BOTH OF US AS WE HAD A FORECAST FROM FSS OF 12000 SCATTERED. NEITHER THE PF NOR MYSELF HAD MUCH EXPERIENCE SHOOTING APCHS TO MINS IN ACTUAL CONDITIONS.