A C172 ON A TRAINING FLT CONFLICTED WITH A BE35 ON DEP WHEN THE STUDENT WAS SLOW TO TURN TO HDG AS CLRED BY DEP CTLR. HIS RESPONSE WAS SLOW BECAUSE HE WAS TRYING TO PROGRAM HIS GPS.

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WE WERE ON AN IFR TRAINING FLT; ON AN IFR FLT PLAN; IN VFR CONDITIONS IN CTLED AIRSPACE. IT IS ALSO IMPORTANT TO NOTE THAT MY STUDENT WAS WEARING A TRAINING HOOD. WE HAD JUST INITIATED THE MISSED APCH FROM THE LOC BACK COURSE RWY 3R WHEN LUK TWR ADVISED US TO 'CLB TO 3000 FT VIA RWY HDG AND CONTACT APCH.' UPON OUR INITIAL CONTACT WITH CINCINNATI APCH; WE WERE IMMEDIATELY ADVISED TO PROCEED DIRECT TO FETEG INTXN. THE STUDENT WAS UNFAMILIAR WITH THE GPS UNIT AND WHILE ATTEMPTING TO LOAD THE NEXT APCH; STARTED A TURN IN THE APPROX DIRECTION OF FETEG. AS PART OF THE STUDENT'S ATTEMPT TO LOAD THE APCH; HE HAD SELECTED DIRECT TO I69; ACTIVATING THE NEW DEST ARPT. THE GPS DREW A LINE FROM OUR PRESENT POS; 3-5 MI NE OF LUK; DIRECT TO I69 (APPROX 100 DEGS). THIS WAS THE COURSE THE STUDENT CONTINUED TO TURN TOWARD. AT THIS POINT; I; AS THE INSTRUCTOR; BEGAN TO TALK THE STUDENT THROUGH LOADING THE RNAV 22 APCH TO I69; IN ORDER TO DETERMINE THE APPROPRIATE COURSE (054 DEGS). BEFORE THE STUDENT COULD GRASP HIS ERROR; CINCINNATI APCH ISSUED AN IMMEDIATE L TURN TO A HDG OF 020 DEGS. HOWEVER; THE STUDENT; THINKING THAT HE WAS PERFORMING THE CORRECT ACTION SELECTED DIRECT AGAIN ON THE GPS AND ROLLED L TO THE INDICATED COURSE DIRECT TO FETEG; 058 DEGS. WHILE EXPLAINING TO THE STUDENT THAT WE HAD BEEN TOLD TO TURN TO AN ASSIGNED HDG OF 020 DEGS; ATC QUERIED OUR HDG; AT WHICH TIME HE RESPONDED THAT WE WERE 'DIRECT FETEG.' ATC QUICKLY ISSUED A L TURN TO 020 DEGS. SHORTLY THEREAFTER; WE WERE CLRED DIRECT FETEG AND CLRED FOR THE RNAV 22 APCH. AFTER THIS EVENT WE WERE TOLD THAT OUR DEV HAD CONFLICTED WITH A BE35 THAT HAD DEPARTED LUK AFTER OUR MISSED APCH. BECAUSE HE WAS TALKING TO LUK TWR AT THE TIME; IT IS NOT KNOWN TO ME HOW CLOSE THIS ACFT ACTUALLY CAME TO OUR POS; HOWEVER; IT IS CLR THAT OUR ERROR DEGRADED THE SAFETY OF FLT IN THIS INSTANCE. HE WAS ISSUED A DEP TURN TO 090 DEGS WITH WHICH OUR DEVIATING FLT PATH CAUSED SEPARATION CONFLICT. AS THE FLT INSTRUCTOR; I SHOULD HAVE BEEN MORE PROACTIVE IN CORRECTING THE DEVIATING FLT PATH. HAVING FLOWN THIS CIRCUIT BEFORE; AND BEING IN VMC; I COULD SEE THAT HE WAS TURNING BEYOND THE REQUIRED HDG. NOT KNOWING WHAT THE ACTUAL DESIRED HDG WAS; I ALLOWED THE DEV TO CONTINUE; THINKING THAT WE WOULD SOON CORRECT OUR PATH. MY SECOND ERROR WAS IN AN ASSUMPTION THAT BECAUSE WE WERE ON A TRAINING FLT; THAT THIS TYPE OF ERROR WOULD NOT DEGRADE THE SAFETY OF FLT; BUT ALLOW THE STUDENT TO LEARN HOW TO MANIPULATE THE GPS WITH MINIMAL CFI ASSISTANCE. THE ERROR OCCURRED WHILE I WAS TALKING MY STUDENT THROUGH THE GPS APCH SET UP. MY THIRD ERROR WAS ALLOWING THE STUDENT TO ROLL OUT ON THE 058 DEG COURSE; KNOWING THAT ATC HAD CLRED US TO A 020 DEG HDG. OUR CLRNC DIRECT TO FETEG HAD BEEN OVERRIDDEN. I SHOULD HAVE BEEN MORE AUTHORITATIVE IN EXERCISING PIC/INSTRUCTOR RESPONSIBILITIES. IT IS CLR TO ME NOW THAT IN AN RNAV EQUIPPED ACFT; CLRED TO AN RNAV FIX; IT IS ASSUMED THAT IF THE CLRNC IS ACCEPTED BY THE PT; THAT ATC EXPECTS IMMEDIATE AND CORRECT PLT ACTIONS. I FEEL THAT THIS SITUATION COULD HAVE BEEN AVOIDED IF I; AS THE INSTRUCTOR; HAD INTERVENED TO ASK ATC FOR AN INITIAL HDG TO THE FIX. THIS WOULD GAVE GIVEN ME ENOUGH TIME TO PROPERLY CONDUCT MYSELF IN A TRAINING ENVIRONMENT; TEACHING THE APPROPRIATE MATERIAL; WITHOUT CREATING AN UNSAFE SITUATION. I COULD HAVE ALSO TAKEN THE FLT CTLS FROM MY STUDENT UNTIL THE SITUATION WAS RECTIFIED. I SHOULD NOT HAVE ASSUMED THAT THIS STUDENT WOULD RESPOND IMMEDIATELY TO MY VERBAL INPUT. ANOTHER ERROR ON MY PART WAS FAILURE TO NOTE THE URGENCY OF THE SITUATION. I DID NOT FEEL A NEED TO RUSH MY STUDENT; AS ATC DID NOT STRESS THE URGENCY OF THE SITUATION. THE FACT THAT THE SECOND ACFT WAS NOT ON MY FREQ DID NOT ALLOW ME TO HEAR ANY ATC INSTRUCTIONS TO HIM. MY INSTRUCTION TO TURN TO 020 DEG HDG WAS GIVEN IN A CALM VOICE; AND WAS NOT FOLLOWED BY ANY LANGUAGE THAT WOULD HAVE LED ME TO BELIEVE MY ACFT WAS IN DANGER. IN THE FUTURE; I WILL NOT BE AS COMPLACENT AS I WAS IN THIS SITUATION. I ALLOWED MY STUDENT TOO MUCH LEEWAY; AND ACCEPT FULL RESPONSIBILITY FOR DOING SO. I SHOULD HAVE STUCK TO MY PERSONAL DEV ALLOWANCES WHICH ARE USUALLY 200 FT ON ALT AND 30 DEGS ON HDG. THIS EVENT CAME AT THE END OF A 10 HR WORK DAY; WHICH ADDED TO THE HAZARD.