C172 ON NIGHT TRAINING FLT HAD UNCTLED TFC PATTERN SEPARATION PROB WITH B737 DEPARTING XING RWY DURING A STOP-AND-GO LNDG.

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IT WAS A CALM; CLR; FULL MOON NIGHT WITH UNLIMITED VISIBILITY. A STUDENT PLT AND I WERE IN THE ARPT TFC PATTERN DOING MULTIPLE STOP-AND-GOES. MY STUDENT JUST FINISHED MAKING AN ANNOUNCEMENT THAT HE WAS ON L XWIND FOR RWY 5 WHEN I HEARD ACR Y ANNOUNCE THAT THEY WERE GOING TO BE TAXIING TO RWY 2. MY STUDENT THEN ANNOUNCED WHEN HE WAS ON L DOWNWIND FOR RWY 5 AND I COULD SEE THE ACR TAXIING TOWARD THE APCH END OF RWY 2. MY STUDENT THEN ANNOUNCED WHEN HE WAS ON L BASE AND TURNING FINAL FOR RWY 5; AND I COULD STILL SEE THE ACR GETTING CLOSER TO THE APCH END OF RWY 2. WHILE WE WERE ON FINAL FOR RWY 5; ACR Y ANNOUNCED THAT THEY WERE TAKING THE ACTIVE RWY 2. I WANTED TO MAKE SURE THEY KNEW WE WERE ON FINAL FOR RWY 5 AND WAS HOPING THEY WOULD NOT MIND US DOING A STOP-AND-GO BEFORE THEY TOOK OFF. SO I GOT ON THE RADIO AND SAID; 'KAHULUI TFC; CESSNA XXX ON FINAL RWY 5; WE WOULD LIKE TO DO A STOP-AND-GO AND THEN GO OVER TO R TFC RWY 2; IF THAT'S OK WITH YOU GUYS.' ACR Y RESPONDED BACK SAYING SOMETHING TO THE EFFECT OF 'SURE; YEAH; OK' (NOT THE EXACT WORDS). WE TOUCHED DOWN ON THE BEGINNING PART OF RWY 5 AND WERE SLOWING DOWN. IN AN EFFORT TO NOT MAKE THE ACR WAIT TOO LONG; WE APPLIED THE PWR TO TAKE OFF BEFORE COMING TO A COMPLETE STOP. AFTER WE WERE AIRBORNE AND PAST THE MAIN TERMINAL (WHICH BLOCKS THE VIEW OF THE APCH END OF RWY 5 FROM RWY 2 AND VICE VERSA); I NOTICED THAT THE ACR JET WAS ALSO AIRBORNE! I PLACED THE AIRPLANE IN A L TURN (AN EARLY L XWIND FOR RWY 5) AND ANNOUNCED THAT I WAS TURING L ON THE RADIO. WHILE BACK ON L DOWNWIND TO RWY 5; ACR Y CAME ON THE RADIO AND SAID SOMETHING LIKE 'YOU DID SAY STOP-AND-GO RIGHT?' I RESPONDED BACK WITH; 'YES I DID SAY STOP-AND-GO; SORRY ABOUT THE CONFUSION; HAVE A SAFE FLT.' THERE WAS NO RESPONSE BACK FROM ACR Y. IN RETROSPECT; I THINK THAT WHEN I SAID 'STOP-AND-GO;' THE ACR Y PLT MUST HAVE THOUGHT I WAS GOING TO STOP ON RWY 5 AND THEN WAIT FOR THEM TO TAKE OFF FROM RWY 2; BEFORE I TOOK OFF AGAIN ON RWY 5. MY PERCEPTION WAS THAT THEY WERE GOING TO GET INTO POS AND HOLD WHILE WE DID OUR STOP-AND-GO. WITHOUT A DOUBT; I SHOULD HAVE MADE SURE WORDS WERE SAID BTWN ME AND THE OTHER ACFT THAT CLARIFIED WHO WAS GOING TO BE AIRBORNE FIRST. A SIMPLE CLARIFICATION LIKE THAT WOULD HAVE PREVENTED THAT CLOSE CALL FROM EVER HAPPENING.