A G-4 FLT CREW EXPERIENCE A FLAP ASYMMETRY FOLLOWED BY LACK OF COOPERATION WITH ATC; FOLLOWED BY A TCASII RA; FOLLOWED BY LOW FUEL WITH A SAFE LNDG AT BAF.

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ON APCH; MY FLT HAD A FLAP ASYMMETRY FAILURE ON THE GIV. ATC WAS NOTIFIED OF THE PROB AND THE NEED TO BREAK OFF THE APCH AND TROUBLESHOOT THE PROB. THE PF TOOK THE RADIOS; NAV; AND ACFT CTL WHILE I HANDLED THE TROUBLESHOOTING; CHKLISTS; AND CALLS TO MAINT AND DISPATCH. THE COCKPIT WAS A BUSY PLACE AND I HAD TO LEAVE MY SEAT TWICE TO GET CHARTS AND EXPANDED CHKLISTS THAT WERE NOT REACHABLE FROM THE SEAT. UPON RETURNING THE SECOND TIME; THE PF TOLD ME THAT WE DIDN'T HAVE ENOUGH FUEL TO RETURN TO OUR HOME MAINT BASE. WE QUICKLY DISCUSSED OPTIONS (WX; WINDS; RWYS LENGTH; AND SVCS) AND SETTLED ON BAF (20 MIN FLT; LONG RWY; INTO THE STRONG SURFACE WINDS; AND APPROPRIATE SVCS). I ADVISED NEW YORK APCH THAT WE NEEDED HIGHER AND DIRECT BAF. THE NEW CTLR (CTLR CHANGE JUST OCCURRED) ASKED WHO WE WERE AND IF WE WERE IFR. (OBVIOUSLY A POOR CHANGE OF CTLRS.) I TOLD HIM WE WERE IFR AND NEEDED HIGHER 'NOW; AND DIRECT BAF.' THIS CTLR STARTED IN ABOUT PREFERENTIAL RTES; ETC. AT THIS TIME MY FLT HAD A CLB RA. THE PF FOLLOWED THE RA AND I ADVISED NEW YORK TRACON OF THE CLB RA AND CANCELING IFR. (IN THE PAST 10 YRS THIS CTLR HAS EARNED THE REPUTATION OF BEING ARROGANT AND UNCOOPERATIVE AND FRANKLY THERE WASN'T FUEL OR TIME TO DEAL WITH HIS ATTITUDE!) I'M VERY CONCERNED ABOUT THE LACK OF CTLR COORD IN NEW YORK TRACON! MY FLT MADE AN EXPEDITIOUS CLB TO AN APPROPRIATE FUEL/TIME CONSERVATION ALT AND CONTACTED ZBW. THE APPROPRIATE CHKLISTS AND BRIEFINGS (FOR CREW AND ATC) WERE COMPLETED. ATC WAS ADVISED OF 'MINIMUM FUEL' AND THE NATURE OF PROB. ZBW; BDL TRACON; AND BAF LCL ALL PROVIDED APPROPRIATE ASSISTANCE SO THAT A SAFE LNDG WAS MADE WITH MINIMUM IFR FUEL RESERVES.