C340 PLT ON IFR APCH HAS NMAC WITH AN AEST TURNING IN ON A 2 MI FINAL.

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ATIS ADVISED IFR TFC COULD EXPECT ILS RWY 33 APCH INTO ADDISON ARPT. APCH CTL VECTORED US TO THE FAF WITH A SHORT TURN-IN; QUICK DSCNT FROM 2500 FT TO 2100 FT AND CLRED FOR THE APCH. VISIBILITY WAS RPTED 4 MI; BUT PROBABLY ONLY 2 MI SLANT RANGE. PLT WAS FLYING HEADS DOWN ON INSTS AND COPLT HANDLING RADIOS AND WATCHING FOR TFC. NONE RPTED. AFTER HDOF TO ADDISON TWR; THEY REQUESTED SLOWER SPD AND PWR WAS REDUCED. REDUCED THEN TO 110 KTS AND DSCNT TO 1300 FT ON GS (MDA IS 894 FT) WHEN COPLT ADVISED TWR THAT APCH NOT GOING TO WORK AS HE HAD SEEN AN AEROSTAR APCHING FROM R; APPARENTLY ON R BASE FOR RWY 33. WHEN PLT THEN SAW ACFT AT 1;30 O'CLOCK POS; SAME ALT; LESS THAN 500 FT AWAY; THEN TURNED R TO GO BEHIND THE AEROSTAR. AT THIS TIME; COPLT REQUESTED INSTRUCTIONS FROM TWR BUT NOT OBTAINED AS TWR'S XMISSION WAS STATIC AND GARBLED; BUT ALL ON OUR ACFT HEARD TWR SAY TO TURN R. TURNED EBOUND; THEN HEARD TWR SAY TO TURN L. PLT AND COPLT AND PAX ALL CONFIRMED AND UNDERSTOOD THIS XMISSION AND WERE CONCERNED AS WOULD PUT ACFT AGAINST TFC ON R DOWNWIND. TWR THEN CALLED AND ASKED WHAT HDG. BY THEN IT WAS 330 DEGS PER THEIR TURN L INSTRUCTIONS. TWR THEN PROCEEDED TO BERATE THE PLTS BECAUSE OF GOING THE WRONG DIRECTION IN TFC PATTERN. WE WERE TOO CLOSE TO ARPT TO TURN L AGAIN; SO DID R 180 DEG TURN INTO DOWNWIND; WAITED ON SINGLE ENG TFC TO LAND; THEN MADE UNEVENTFUL LNDG.