DURING AN INST RATING TRAINING FLT; INSTRUCTOR PLT ALLOWED TRAINEE TO MAKE A TOUCH AND GO UPON COMPLETION OF AN ILS APCH CONTRARY TO TWR INSTRUCTIONS FOR A LOW PASS ONLY. INSTRUCTOR PLT WAS BUSY GIVING INSTRUCTIONS TO TRAINEE AND DID NOT HEAR THE TWR INSTRUCTIONS RESULTING IN TWR MOVING ANOTHER ACFT IN TRAIL TO ANOTHER RWY.

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A STUDENT AND I WERE ON AN IFR TRAINING FLT XCOUNTRY TO GREER; GSP; SC. PROBS HAD ARISEN WITH THE ATC FROM THE BEGINNING OF THE FLT. WE WERE ON AN IFR FLT PLAN BUT ATC WAS CONFUSING IN ITS CLRNCS BY GIVING US MIXED VFR AND IFR CLRNCS. AFTER STRAIGHTENING OUT THE FLT PLAN; WE WERE CLRED FOR A PRACTICE ILS RWY 21 APCH INTO GSP AND HANDED OFF TO THE TWR. TWR CLRED US FOR THE OPTION PRIOR TO GS INTERCEPTION AND WE PROCEEDED WITH THE APCH. THE STUDENT BECAME OVERWHELMED WITH ALL THE TASKS AT HAND; INCLUDING COMS. I WAS BUSY EXPLAINING THE APCH AS HE FLEW IT AND WAS MONITORING COMS WITH THE TWR. SOMEWHERE DURING THIS TIME; TWR APPARENTLY RADIOED TO US AND 'ADVISED' US TO DO A LOW PASS. MY STUDENT HAD MADE A QUICK RADIO STATEMENT; BUT COULDN'T REMEMBER WHAT WAS SAID. DECISION HT WAS REACHED AND WE DID A VERY QUICK TOUCH AND GO AS PER THE PREVIOUS CLRNC THAT I HAD RECEIVED. AFTER WE LIFTED OFF; TWR INSTRUCTED A FLT BEHIND US TO TURN TO THE W SO HE COULD BRING HIM IN BEHIND ANOTHER ACFT BEHIND HIM. AT THIS TIME; TWR CAME ON THE RADIO AND TOLD US TWICE THAT HE HAD 'ADVISED' US TO DO A LOW APCH ONLY. CONTRIBUTING FACTORS: ATC'S APPARENT LACK OF COORD WITH OUR ACTIVATED AND PRE-FILED IFR FLT PLAN; UNCLR RADIO INSTRUCTIONS AND READBACKS FROM BOTH ATC AND OUR ACFT; FATIGUE EXHIBITED IN BOTH PLTS. POSSIBLE CORRECTIVE ACTIONS: BETTER ATC INSTRUCTIONS; BETTER PLT SITUATIONAL AWARENESS (MYSELF). THE PRACTICE APCH COULD HAVE BEEN SPED UP BY ATC OR MYSELF TO ACCOMMODATE TFC FLOW.