WHEN LTT ACR FLC IS UNABLE TO COMPLY WITH CLRNC; TRACON CTLR MAKES INCORRECT CTL DECISION; COMING INTO CONFLICT WITH OTHER ACR TFC ON VECTOR TO MIA AND FLL ARPTS. LTT MAKES TCASII EVASIVE MANEUVERS FURTHER COMPLICATING CTLR DECISION PROCESS.

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WE (ACFT W) WERE ON AN IFR FLT FROM MIA TO FPO WITH AN INITIAL DEP TO THE W. MIA DEP INFORMED US THAT SINCE WE 'WERE NOT CLBING FAST ENOUGH;' THAT WE WOULD BE HELD INITIALLY AT 5000 FT AND INSTRUCTED US TO TURN E. OUR FLT PATH TOOK US APPROX 3 MI S OF FLL WHICH IS AN UNUSUAL LOCATION FOR A DEP FROM MIA FOR THE GIVEN ALT. AFTER PASSING THE SHORELINE WE WERE INSTRUCTED TO INTERCEPT THE 058 DEGS OFF OF VKZ AND PROCEED TO THE PADUS INTXN. THE SIGNAL RECEPTION FROM VKZ WAS INTERMITTENT AND THE SELECTED RADIAL (058 DEGS) WAS SHIFTING ON THE DISPLAY; HOWEVER; WE DID NOT FEEL THAT IT WAS DRASTIC ENOUGH TO RPT A LOSS OF NAV TO ATC. IN ORDER TO MINIMIZE THE DEV; WE HAD THE 100 MI RANGE SELECTED IN THE DISPLAY. SHORTLY AFTER TURNING NE; WE NOTICED APCHING TFC AT OUR 10 - 11 O'CLOCK POS -- ONE ABOVE US (ACFT X) AND ONE BELOW US (ACFT Y). BEFORE WE COULD QUERY ATC ABOUT THE TFC; THE CTLR INFORMED US THAT WE WERE N OF THE ASSIGNED RADIAL (WHICH WAS DUE TO OUR 'EYEBALLING' THE RADIAL) AND THAT THERE WAS A TFC CONFLICT. HE INSTRUCTED US TO MAKE AN IMMEDIATE CLBING TURN TO THE L SINCE THE TFC (BELOW AND DSNDING) WAS TURNING W FOR FINAL INTO FLL. WE ACHIEVED VISUAL CONTACT WITH THE B737 AND RECEIVED A TA FROM THE TCASII AND INFORMED MIA DEP. HE THEN INSTRUCTED US TO MAKE A R TURN IMMEDIATELY (WHICH WAS TURNING US INTO THE ONCOMING TFC. HOWEVER; NO MORE TA'S WERE ISSUED). THE CTLR THEN BROADCAST '[EXPLETIVE] YOU HAVE ANOTHER ONE (ACFT Z) AT 10 O'CLOCK' (ABOVE AND DSNDING) AND INSTRUCTED US TO MAKE ANOTHER IMMEDIATE TURN L (AGAIN INTO ONCOMING TFC) SHORTLY FOLLOWED WITH A R TURN AND AN INSTRUCTION TO STOP OUR CLB. WE THEN RECEIVED MORE TURNS RANGING FROM N TO S IN RAPID SUCCESSION IN ORDER TO GET US AWAY FROM THE B757 (ACFT Z) WHICH WE HAD VISUAL CONTACT WITH. (NO FURTHER TA OR RA ISSUED OTHER THAN THE ORIGINAL ONE MENTIONED.) AFTER CLRING THE TFC THE REMAINDER OF THE FLT WAS ROUTINE. I BELIEVE SOME OF THE CONTRIBUTING FACTORS ARE AS FOLLOWS: 1) IT WAS MY 6TH CONSECUTIVE DAY OF DUTY CAUSING MENTAL FATIGUE. 2) THE UNUSUAL DEP LOCATION AND ALT. 3) OUR ESTIMATING THE LOCATION OF THE SHIFTING RADIAL. 4) LATE RESPONSE OF US TO QUERY TFC AND ATC ADVISING US OF TFC. 5) ATC'S INDECISIVENESS AS TO AN EVASION RTE. 6) LACK OF COM BTWN MIA AND FLL.