B757 FLC UNABLE TO ACCEPT VECTOR FROM APCH CTLR DUE TO TSTMS. APCH CTLR IS INSISTING ON THE TURN SO FLC ATTEMPTS TO ACCOMMODATE WITH A TIGHT DSNDING TURN THEN BACK ON THE LOC COURSE. TCASII TA ACTIVATES.

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ON APCH TO MIA; WITH TSTMS IN THE AREA; ZMA AND MIA APCH CTL WERE VERY BUSY VECTORING ACFT AROUND STORMS. COPLT FLYING. WHILE ON CYPRESS ARR MIA APCH CTL CLRED US TO 4000 FT; ISSUED HDG OF 120 DEGS TO INTERCEPT RWY 9R LOC. THERE WERE TSTMS JUST BEYOND THE RWY 9 LOC COURSE TO THE SE. IT WOULD BE A TIGHT TURN; BUT POSSIBLE TO TURN INSIDE THE STORMS. JUST PRIOR TO INTERCEPT; MIA APCH CTL ISSUED A HDG OF 150 DEGS WHICH WOULD TAKE US INTO THE STORM NOW PAINTING PURPLE ON OUR RADAR. WE WERE ALSO STILL VMC AND COULD SEE THE STORM CLRLY. CAPT INFORMED MIA APCH CTL THAT WE COULD NOT TURN THAT DIRECTION. MIA APCH CTL WAS ADAMANT THAT WE TURN TO 150 DEGS. CAPT INFORMED MIA APCH CTL WE WOULD HAVE TO TURN FURTHER TO THE S TO AVOID THE WX. WE MADE A HIGH ANGLE OF BANK DSNDING R-HAND TURN AND RE-INTERCEPTED MIA RWY 9R LOC COURSE AS WE COMPLETED THE TURN. THE CTLR WAS STILL INSISTING THAT WE TURN BACK L DURING OUR R-HAND TURN IN ORDER TO INTERCEPT THE RWY 9R LOC COURSE. THIS WOULD CLRLY JEOPARDIZE THE SAFETY OF THE ACFT BECAUSE IT WOULD PUT US IN THE TSTM. WE DID RECEIVE A TA ON TCASII AND VISUALLY ESTIMATED PROX OF 3 NM. CONTINUED TO NORMAL LNDG.