RPTR; AN OBSERVER DURING A TYPE RATING RIDE ON A CE560; EXPERIENCES A RWY EXCURSION WHEN THE FLT CREW LOSES CTL DURING A SIMULATED ENG FAILED LNDG PROC AT ZZZ.

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I WAS A PAX ON THIS TYPE RATING CHK RIDE; INVITED ALONG BY THE EXAMINER TO GAIN MORE EXPERIENCE IN 2-PLT CRM. THE COPLT WASN'T HELPING HIS PLT; THE APPLICANT. LATER THE DESIGNATED PLT EXAMINER STATED THE COPLT WAS NOT ALLOWING THE APPLICANTS TO BE PIC. I SAW THE SAME BEHAVIOR; THE COPLT TRYING TO TELL THE APPLICANT (PLT) WHAT TO DO AND HOW TO DO IT. THE CRM CONCEPT BECAME CRYSTAL CLR DURING ONE LNDG. IT WAS A SIMULATED SINGLE ENG LNDG; ALLOWING ONLY A SINGLE THRUST REVERSER. I WAS SITTING IN THE SECOND COUCH SEAT AND THOUGHT THE PLANE WASN'T SLOWING VERY WELL; EVEN WITH THE THRUST REVERSERS. I LOOKED OUT THE WINDOW AND WAS SURPRISED TO SEE THE SPD BRAKES RETRACTED. THE COPLT TOOK OVER AND DEPLOYED THE SECOND THRUST REVERSER; WHEN THE ACFT SWERVED VIOLENTLY AND I WAS THROWN AGAINST THE SEATBELT. AS I LOOKED OUT; I SAW WE HAD SWERVED ONTO THE TXWY NO-XGRESSION ZONE; BUT WERE NOT STOPPING. WE 'FLUSHED' AN R-22 AND SPOOKED A SECOND AS WE SWERVED INTO THE HELI PARKING AREA. IF THE INSTRUCTOR ON BOARD THAT FIRST R-22 HADN'T SEEN US COMING AND DEPARTED WITHOUT A TKOF CLRNC; WE WOULD HAVE RUN THEM OVER. THE DESIGNATED PLT EXAMINER WAS SAYING 'CAN WE STOP? CAN WE STOP? USE THE EMER BRAKE....' WE HAD A NICE BURNT RUBBER SMELL IN THE PAX COMPARTMENT AS WE STOPPED. THE DESIGNATED PLT EXAMINER DIRECTED A SHUTDOWN (HAD TO SAY IT TWICE). I EVACED WITH THE DESIGNATED PLT EXAMINER ON MY HEELS. WE DISCOVERED WE STOPPED WITHIN 10 FT OF A LINE OF PARKED ACFT. THE TIRE HAD NOT BLOWN; BUT THE BRAKE WAS HOT. THE FIRST MECH THAT ARRIVED FROM THE REPAIR STATION DEEMED THE BRAKE FAILURE WAS DUE TO LOW HYD FLUID. AFTER THE OUTFIT'S CHIEF MECH HAD SIGNED OFF THE PLANE AFTER AN INSPECTION AND FLUID FILL; THE RIDE CONTINUED WITHOUT FURTHER INCIDENT.