A320 FLT CREW HAS A TCAS RA DURING DEP FROM MDPC.

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I WAS OPERATING AS CAPT AND PNF. OUR ATC CLRNC WAS PNA W10 PIXAR UA636 KOBET UG446 GTK AS FILED; CLB AND MAINTAIN FL340 SQUAWK XXXX CONTACT DEP ON XXX.XX WHEN AIRBORNE. AT 300 FT I CALLED DEP. THEY INFORMED ME THAT WE WERE GIVEN THE WRONG FREQ. AT 1000 FT MSL I CALLED THE NEW FREQ AND RPTED OUT OF 1000 FT FOR FL340. WE WERE TOLD TO STAND BY. HE THEN GAVE SOMEONE A CLRNC TO 3000 FT. AS WE CLBED THROUGH 2700 FT TCAS GAVE US A 'TFC' WARNING AND AN AMBER TFC DISPLAY AT 1-2 O'CLOCK POS 3-4 NM +500 FT DSNDING. I IMMEDIATELY TOOK THE CTLS AND MADE A LEVELOFF AT 2900 FT MSL. AT THIS POINT THE FO WAS LOOKING OUT FOR THE TFC; WE WERE IN AND OUT IMC. WE SAW AN ATR MAKING A CLBING L TURN AWAY FROM US AND HE WAS RPTING A CLB DUE TO COLLISION AVOIDANCE. THE CTLR AND THE ATR WERE THEN ARGUING ABOUT THEIR CLRNC. THE CTLR SAID THAT HE ISSUED A DSCNT TO 4000 FT AND TO ENTER A R DOWNWIND. (FIELD WX WAS 700 FT OVCST. NO VFR DOWNWIND POSSIBLE.) THE ATR SAID THAT THEY WERE GIVEN 3000 FT AND TO TRACK INTO THE PNA VOR ON THE 112 DEG RADIAL. WE KEEP TRYING TO GET A WORD IN TO CONFIRM WHAT ALT AND DIRECTION HE WANTED US TO FLY. AFTER 3 ATTEMPTS HE FINALLY TOLD US TO MAINTAIN 3000 FT. AFTER HE AND ATR WERE DONE ARGUING; WE WERE TOLD TO PROCEED TO PIXAR AND 15000 FT. NO FURTHER EVENT. SEPARATION WAS DOWN TO 300 FT VERT AND APPROX 2 NM LATERALLY.