ON A PRACTICE ILS RWY APCH; A LATE CHANGE TO FTW TWR; A PRACTICE ENG OUT PA31 RESULTS IN A TFC PATTERN NMAC WITH AN F90 XING IN FRONT FOR ANOTHER RWY.

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I WAS IP (INSTRUCTOR PLT) IN THE NAVAJO ON A VFR TRAINING FLT. WE HAD BEEN VECTORED TO FINAL; RWY 34 AT FTW. APCH WAS INFORMED WE WERE SIMULATED SINGLE-ENG ON THE APCH. APCH HAD ADVISED US OF A CESSNA 210 MANEUVERING E OF THE LOC. WE WERE VECTORED OFF THE APCH AND BACK TO THE LOC AND CLRED FOR THE PRACTICE ILS RWY 34 APCH. THE STUDENT ASKED FOR FREQ CHANGE TO TWR ABOUT 2 MI PAST THE OM. AT THE TIME OF FREQ CHANGE; I OBSERVED THE F90; TURNING R BASE; DIRECTLY INTO OUR FLT PATH. THE KING AIR CROSSED OUR FLT PATH; TO A POS SLIGHTLY ABOVE AND AHEAD OF OUR NAVAJO. TWR INSTRUCTED US TO SIDESTEP TO THE L (INTO THE KING AIR) FOR A LNDG ON RWY 35. I TOOK CTL OF THE NAVAJO; RESTORED PWR ON THE RETARDED ENG; AND ATTEMPTED EVASIVE MANEUVERING. THE KING AIR CONTINUED; APPARENTLY OBLIVIOUS TO THE SIT; TO A LNDG. WE LANDED THE NAVAJO SUCCESSFULLY ON RWY 35. AFTER LNDG; I ASKED GND IF LCL HAD RECEIVED A HDOF FROM APCH. THE RESPONSE WAS THAT LCL HAD BEEN TRYING TO CONTACT US. I SUPPOSE NO HDOF WAS EFFECTED. BY THE GRACE OF GOD; I AVOIDED A MIDAIR COLLISION; CAUSED BY AN APPARENT BREAKDOWN OF PROCS AND/OR COM BTWN APCH (DFW) AND FT WORTH MEACHAM TWR. IN MY OBSERVATION; THE KING AIR SHOULD HAVE BEEN INSTRUCTED TO EXTEND DOWNWIND TO FOLLOW THE NAVAJO ON FINAL. THE KING AIR CREW FAILED TO EXERCISE SEE AND AVOID; AND TO GIVE PRIORITY TO AN AIRPLANE ON FINAL.