C172 PLT HAS AN NMAC WITH ANOTHER ACFT WHILE IN THE PATTERN AT ILG.

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WHILE CONDUCTING PVT PLT TRAINING IN ACFT X AT ILG; I EXPERIENCED AN NMAC WITH A C130 ACFT IN THE PATTERN UNDER THE CTL OF THE ILG TWR. AFTER INITIAL CONTACT WITH THE TWR IN WHICH I ADVISED WE WERE GOING TO BE REMAINING IN THE PATTERN FOR PATTERN WORK; TWR ADVISED TO ENTER L DOWNWIND FOR RWY 27. AFTER ADVISING TWR OF OUR POS ON THE DOWNWIND; TWR REQUESTED US TO EXTEND THE DOWNWIND FOR ANOTHER ACFT (C130 ALSO CONDUCTING PATTERN WORK) AND THAT TWR WOULD CALL OUR TURN TO BASE FOR RWY 27. AFTER EXTENDING OUR DOWNWIND APPROX 3 MI OUT; TWR ADVISED US TO TURN TO BASE. WE COMPLIED AND TURNED BASE AND CONTINUED TO SET UP FOR LNDG. WE NEXT TURNED TO FINAL FOR RWY 27 WHEN I NOTICED THE AFOREMENTIONED C130 TURNING BASE POSITIONING US FOR #2 TO THE ARPT. TWR THEN ADVISED ME TO 'TURN R 270 DEGS;' AND I REPLIED 'R 360 DEGS FOR ACFT X.' I WAS ALREADY ON A FINAL APCH HDG OF 270 DEGS TO RWY 27 SO THE MOST LOGICAL ACTION TO ALLOW FOR SPACING WAS TO TURN R 360 DEGS. TWR THEN CAME BACK AND SAID SOMETHING TO THE EFFECT OF 'TURN R; YOU'RE GOING TO HIT THE C130.' I MAINTAINED VISUAL CONTACT WITH THE C130 THE WHOLE TIME AND REALISTICALLY WAS NOT IN DANGER OF HITTING THE C130 BUT WOULD HAVE NOT BEEN ABLE TO EXECUTE A TOUCH-AND-GO BECAUSE OF WAKE TURB AND THE AMOUNT OF TIME IT WOULD TAKE FOR C130 TO CLR THE ACTIVE. I CONTINUED WITH MY ORIGINAL INTENTION OF EXECUTING A R 360 DEG TURN AND THEN CALLED TWR AGAIN TO CONFIRM MY TURN WHEN PASSING THROUGH A HDG OF 350 DEGS. TWR THEN STATED 'WELL CONTINUE ON NOW BACK TO RWY HDG AND YOU'RE CLRED FOR THE OPTION RWY 27.' THIS SITUATION COULD BE PREVENTED IN THE FUTURE IF THE CTLRS AT ILG TWR EXHIBIT MORE SITUATIONAL AWARENESS OF THE ACFT IN THE PATTERN AND BY MAINTAINING A PARTICULAR SEQUENCE THAT WAS ALREADY ESTABLISHED INSTEAD OF MAKING THE IMPROMPTU CHANGES.