FLT CREW OF PIAGGIO 180 BLOW TIRE ON LNDG FOLLOWING AN UNSTABILIZED APCH PUNCTUATED WITH STALL WARNINGS; ABOVE GS INDICATIONS AS WELL AS EXCESSIVE SINK RATES. LATE INTERCEPT VECTOR BY APCH CTLR CONTRIBUTED TO ABOVE GS CONDITION.

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I WAS ACTING AS THE PNF ON BOARD THE ACFT AND WAS ON THE REPOSITIONING FLT FROM BUR-CRQ. THIS WAS THE SECOND DAY OF MY 7 DAY ROTATION AND MY IOE CAPT WAS ON 4TH DAY. WE WERE RESTED 8 HRS THE NIGHT BEFORE AND ON THE DAY OF THE INCIDENT IT WAS OUR 4TH LEG OF THE DAY. AT THIS TIME OUR FLT TIME WAS 4 1/2 HRS. DURING THE LNDG PHASE AT CRQ; ACFT R MAIN TIRE AND WHEEL ASSEMBLY SUSTAINED DAMAGED DUE TO UNKNOWN CAUSES. PRIOR TO DEPARTING BUR; I HAD ASKED THE IOE CAPT IF SHE WAS COMFORTABLE FLYING FROM THE R SEAT. IOE CAPT'S RESPONSE WAS 'YES.' WHILE PROCEEDING INBOUND TO CRQ; THE SOCAL APCH CTLR VECTORED US THROUGH THE ILS RWY LOC AND THEN GAVE US ANOTHER VECTOR TO RE-INTERCEPT. THIS PUT US ABOVE THE GS. THE WX WAS BETTER THAN RPTED 5000 FT BROKEN; 10 MI VISIBILITY; LIGHT RAIN; WINDS WERE 150 DEGS AT 7 KTS; ENABLING US TO ACCEPT THE VISUAL APCH. AS WE SWITCHED FREQ FROM SOCAL TO CRQ TWR; TWR INFORMED US TO SLOW TO 140 KTS DUE TO TFC ON FINAL APCH. ON 3/4 MI FINAL; THE PAPI LIGHTS WERE INDICATING ALL WHITE; GIVING A CLR INDICATION OF BEING TOO HIGH. I STATED; 'WE ARE TOO HIGH.' THE IOE CAPT REPLIED; 'WE'LL MAKE IT.' I BEGAN CALLING VREF AND SINK RATE; WHICH WAS APPROX 1500 FPM. THE IOE CAPT ATTEMPTED TO CORRECT. ABOVE THE LNDG THRESHOLD WITH THE ACFT OBVIOUSLY TOO HIGH; I CALLED VREF -1; -2; -3; +1; +2; +3; ETC; AND THE FIRST STALL WARNING INDICATION CAME ON. THE IOE CAPT CORRECTED BY ADDING PWR AND PITCHING THE NOSE DOWN. SOON AFTER ANOTHER STALL WARNING CAME ON DURING FLARE WHICH WAS APPROX 10 FT ABOVE THE RWY. I WAS CALLING FOR VREF AND SINK RATE WHICH WAS FOLLOWED BY WHAT I FELT WAS LNDG IN A STALLED CONDITION. THE RWY WAS DRY WITH A 7 KT 90 DEG XWIND FROM THE L. AFTER MAIN GEAR CONTACT WITH THE RWY; THE ACFT VEERED SHARPLY TOWARD THE R. THE IOE CAPT WAS FIGHTING THE CTLS AS THE ACFT WAS NOW SWINGING R AND L. THE IOE CAPT PUT THE PROPS IN REVERSE IN AN ATTEMPT TO REGAIN DIRECTIONAL CTL. THIS ACFT WHEN PUT INTO REVERSE; HAS A TENDENCY FOR THE R ENG TO GO INTO REVERSE FIRST. IN ORDER TO MAINTAIN SYMMETRIC REVERSE THRUST; THIS ACFT REQUIRES THE PWR LEVER TO BE SPLIT 1/2 INCH TO 1 INCH. THE IOE CAPT HAD THE PWR LEVER IN THE PARALLEL POS RESULTING IN ASYMMETRICAL THRUST FAVORING THE R ENG; PULLING THE ACFT TO THE R. AT THIS TIME; THE ACFT WAS SEVERELY VIBRATING; MAINTAINING DIRECTIONAL CTL WAS EXTREMELY DIFFICULT. AS THE ACFT WAS OBVIOUSLY HEADING OFF THE R SIDE OF THE RWY; I APPLIED FULL L RUDDER. AT THIS TIME; DEP OFF THE RWY BECAME IMMINENT; SO I ENGAGED THE STEERING SYS; WHICH ENABLED THE ACFT TO STAY ON THE RWY AND COME TO A COMPLETE STOP. I PERFORMED AN EMER SHUTDOWN TO SECURE AND AVOID FURTHER DAMAGE TO THE ACFT. THE RWY WAS THEN SHUT DOWN AS WE WERE INFORMED BY THE TWR THAT WE HAD BLOWN A R MAIN TIRE. AFTER SECURING THE AIRPLANE; THE ARPT AUTH APCHED US AND ASKED FOR A SIGNATURE FROM THE PERSON IN CHARGE OF THE ACFT. THE IOE CAPT STATED THAT I WAS PIC AND WAS RESPONSIBLE FOR THE ACFT. I WAS TOLD TO SIGN FOR THE ACFT'S REMOVAL. I WAS TAKEN BY SURPRISE AS I HAD THE UNDERSTANDING THE IOE CAPT WAS ULTIMATELY RESPONSIBLE FOR THE OP OF THE ACFT UNTIL MY LINE TRAINING WAS COMPLETED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THE P180 HAS NO ANTISKID SYS AND HE FELT THAT EXCESSIVE BRAKE APPLICATION AFTER TOUCHDOWN FOLLOWING THE UNSTABILIZED APCH WAS LIKELY THE CAUSE OF THE TIRE FAILURE. RPTR ADVISED THAT HIS RPT TO THE COMPANY SAFETY OFFICER REGARDING THE ACTIONS OF THE IOE CAPT DURING AND SUBSEQUENT TO THIS INCIDENT RESULTED IN THE CAPT'S REMOVAL FROM ALL FLT DUTIES. SHE CONTINUES WITH THE COMPANY IN THE CAPACITY OF A GND INSTRUCTOR. THE SANCTION WAS BASED ON BOTH THE FAILURE TO ABANDON THE UNSTABILIZED APCH AND THE IMPROPRIETY OF PRESSURING THE RPTR TO ASSUME RESPONSIBILITY FOR THE FLT AND THE ACFT CONTRARY TO HIS ROLE AS A PLT IN TRAINING.