AN FK100 FLC FINDS THAT THE ATTITUDE OF THE ZID ENRTE CTLR IS RATHER STRANGE WHEN CTLR PERSISTS IN ACCUSING CREW OF DEVIATING FROM THE AMENDED CLRNC DURING TSTM AVOIDANCE NEAR J-6 NE OF LIT; AR.

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VECTOR GIVEN TO JOIN RWY 18R ILS; ALL CHKLISTS DONE AND ACFT DSNDING; SET UP; AND CONFIGURED FOR PHASE OF FLT; ON AUTOPLT. WHEN CLRED FOR APCH; FO SELECTED LNAV INSTEAD OF 'APCH MODE.' ACFT PROMPTLY MADE HARD TURN TO THE L TO FLY TO LAST WAYPOINT (OFF L WING). CREW MOMENTARILY SURPRISED BY WRONG TURN AND ITS CAUSE. CAPT HIT HDG SELECT TO RETURN TO ORIGINAL HDG ASSIGNED FOR INTERCEPT; BUT AUTOPLT WAS VERY SLOW IN STOPPING TURN AND STARTING R TURN. FO CLICKED OFF AUTOPLT TO LIGHTEN TURN AND WAS DISTR BY EVENTS TO THE POINT THAT HE ADDED PWR FOR THE 3000 FT LEVELOFF WITH SPD BRAKE STILL UP. CAPT LOWERED SPD BRAKE FOR FO BUT ACFT DSNDED 200-300 FT BELOW 3000 FT ASSIGNED AND CROSSED RWY CTRLINE AT AROUND 75 DEGS OFF INBOUND COURSE. WE DEFINITELY VIOLATED THE RWY 18L APCH PATH DURING CORRECTIONS. (RWY 18L NOT IN USE FOR LNDGS AT THE TIME.) CAPT REQUESTED AND RECEIVED CLRNC FOR VISUAL APCH DURING CORRECTIONS. LESSONS LEARNED: 1) PROGRAM AUTOFLT SYS PROPERLY TO START. 2) DON'T TROUBLESHOOT SYS WHEN CLOSE IN -- KICK IT OFF AND BE PREPARED TO HAND FLY IT. 3) DON'T BE COMPLACENT BECAUSE OF ROUTINE NATURE OF APCH; WX AND CREW PERFORMANCE.