FLC OF CPR ACFT UNABLE TO ACCEPT VISUAL. CLRED TO HDG AND ALT. FREQ CROWDED. UNABLE TO ADVISE CTLR OF BREAK ALLOWING A VFR APCH. FLT TURNED AND DSNDED.

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15 MI NW OF ARPT. IN CONTACT WITH MIA APCH CTL; INFORMED APCH CTL OF ARPT IN SIGHT AND REQUESTED A VISUAL APCH. APCH GAVE US A 180 DEG HDG AND MAINTAIN 4000 FT. FT LAUDERDALE WAS USING 9L AT THE TIME. AFTER SEVERAL MINS ON THIS HDG; WHILE APCH WAS WORKING A FOREIGN CARRIER OUT OF MIA; HE CLRED US FOR A VISUAL APCH TO 9L. AT THIS TIME DUE TO SEVERAL SMALL CLOUD BUILDUPS BETWEEN US AND THE ARPT I HAD TO INFORM APCH THAT WE COULD NOT ACCEPT A VISUAL APCH. HE TOLD US TO MAINTAIN HDG AND ALT AND WENT BACK TO THE FOREIGN CARRIER WHO WAS ASKING QUESTIONS ABOUT HIS CLRNC. AT THE SAME TIME WE COULD SEE A SMALL TSTM WITH VISIBLE LIGHTNING IN OUR 12 O'CLOCK POS ABOUT 10 MI. NOT BEING ABLE TO CONTACT APCH CTL BECAUSE OF THE FREQ BEING TIED UP BY APCH AND THE FOREIGN CARRIER AND THE FACT THAT WE COULD NOT CONTINUE ON OUR 180 HDG MUCH LONGER AND THAT WE HAD A BREAK IN THE CLOUDS RIGHT AT THE EXTENDED CENTERLINE FOR 9L AT FLL AND GOOD VFR FROM THAT POINT; ALL THE WAY TO THE ARPT; THE CAPT DECIDED TO TURN TO THE ARPT AND BEGIN A VISUAL APCH. AT THE SAME TIME I ATTEMPTED AGAIN TO CONTACT APCH CTL BUT WAS AGAIN BLOCKED BY THE OTHER CARRIER. I THEN SWITCHED TO FLL TWR AND INFORMED THEM THAT WE WERE ON A VISUAL APCH TO 9L. THE TWR CTLR TOLD US THAT APCH CTL WANTED US BACK ON THEIR FREQ AND THAT WE WERE NOT CLRED FOR THE APCH. I THEN ASKED TWR TO CANCEL OUR IFR AND PERMISSION TO LAND VFR WHICH WAS GIVEN WITH THE MESSAGE THAT WE CALL APCH CTL ON THE LANDLINE. WE SHOULD HAVE INFORMED FLL TWR THAT WE HAD NOT CANCELLED IFR WITH APCH -- OR EVEN BETTER; STAYED WITH APCH FOR VECTORS AROUND FOR ANOTHER APCH. I FEEL THAT FATIGUE HAD SOME EFFECT ON OUR JUDGEMENT -- WE WERE COMPLETING AN ALL NIGHT TRIP FROM THE WEST COAST.