ALT DEV ALT OVERSHOT WITH A HDG TRACK DEV DURING AN IAP VOR APCH MISSED APCH PROC WITH A SIMULATED INFLT ENG SHUT DOWN. POTENTIAL CONLICT LTSS ENSUED WITH ACFT Y ON APCH.

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PIC WAS CONDUCTING IFR TRAINING FLT IN AN SMT TWIN WITH SINGLE FLT CTLS AND HAVING STUDENT FLY THE VOR-A APCH TO GNV. AT MDA (900 FT MSL) INSTRUCTOR SIMULATED ENG OUT AT APPROX 2 MI FROM ARPT. STUDENT ENGAGED IN APPROPRIATE ENG OUT ACTION INCLUDING CLEAN UP OF PLANE AND CLBOUT FOR PUBLISHED MISSED APCH; HOWEVER; STUDENT WAS SLOW IN MAKING L TURN TO PUBLISHED MISSED APCH HDG DUE TO THE DISTR OF THE SIMULATED ENG OUT AND A RELUCTANCE TO MAKE STANDARD RATE TURNS WITH SIMULATED ENG OUT. IN ADDITION; STUDENT ASSUMED IT WOULD BE SAFER TO OBTAIN ADDITIONAL ALT DUE TO SIMULATED ENG OUT AND PROCEEDED TO CLB THROUGH THE PUBLISHED MISSED ALT OF 2000 FT MSL. THE INSTRUCTOR; BEING OCCUPIED WITH THE ENG OUT PROC NOTICED THE OVERCLB AT APPROX 2800 FT MSL AND INSTRUCTED AN IMMEDIATE DSCNT TO 2000 FT WHICH THE STUDENT ACCOMPLISHED. THE INSTRUCTOR THEN RETURNED THE SIMULATED OUT ENG TO SVC AND NOTICED THAT THE STUDENT; DUE TO THE DISTRACTING CIRCUMSTANCES; HAD CONTINUED THE L TURN THROUGH THE PUBLISHED 295 DEG HDG TO A HDG OF APPROX 245 DEG. AT THIS TIME; ATC ADVISED AN IMMEDIATE TURN TO 360 DEG FOR VECTORS TO THE HOLD AT DRAFT INTXN AND ASKED THAT ATC BE NOTIFIED BY PHONE DUE TO A POSSIBLE PLT DEV. LATER CONVERSATIONS WITH ATC INDICATED THAT THE FLT PATH HAD BROUGHT THE ACFT WITHIN 4.75 NM OF ANOTHER ACFT ON AN IFR FLT PLAN WHICH WAS INBOUND FOR GNV ARPT AND HAD RECEIVED A CLRNC FOR A VISUAL APCH TO LAND. FACTORS CONTRIBUTING TO THE INCIDENT INCLUDED THE SIMULATED ENG OUT; THE DISTR TO STUDENT AND INSTRUCTOR FROM THE OVERCLB AND DSCNT; RETURN OF SIMULATED OUT ENG AND THE NON-DUAL CTL CONFIGN OF THE ACFT WHICH FORCED THE INSTRUCTOR TO COACH THE STUDENT THROUGH THE CORRECTIONS RATHER THAN TAKE MORE IMMEDIATE RECOVERY ACTIONS.