AN MLG CREW; DEPARTING LGA; UPON BEING ISSUED A L TURN; STARTED A R TURN INSTEAD!

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DEPARTED LGA AT XA46Z. RWY 13 WHITESTONE CLB. WX WAS OVCST; RAIN; NUMEROUS TSTMS IN VICINITY WITH 1 CELL LOCATED 8-10 MI E OF LGA ON EXTENDED CTRLINE OF RWY 13. DEP PROC CALLED FOR IMMEDIATE R TURN TO HDG 180 DEGS. THIS TURN WAS MADE PROPERLY. PROC THEN CALLED FOR A L TURN TO 040 DEGS AT LGA 2.5 DME. JUST AS FO WAS ABOUT TO START THE L TURN TO 040 DEGS; NEW YORK DEP SAID 'TURN L TO 310 DEGS.' I SET HDG BUT TO 310 DEGS. IT WAS TURNED TO THE L. AS THIS WAS MORE THAN A 180 DEG TURN; THE FLT DIRECTOR COMMANDED A R TURN TO 310 DEGS (THE SHORTEST WAY). THE FO; PF; INCORRECTLY FOLLOWED THE FLT DIRECTOR. ACFT TURNED R TO ABOUT 240 DEGS BEFORE I AND NEW YORK DEP NOTICED INCORRECT DIRECTION OF TURN. BOTH THE CAPT AND ATC DIRECTED A L TURN TO 310 DEGS. L TURN WAS THEN MADE. NO SEPARATION WAS LOST. FLT PROCEEDED UNEVENTFULLY. CONTRIBUTING FACTORS: FO WAS ON HIS IOE TRIP ON THE B737. WX: NUMEROUS TSTMS IN IMMEDIATE VICINITY; SPECIFICALLY ON EXTENDED CTRLINE OF DEP RWY WITH LOW OVCST AND RAIN. PNF; CAPT; DISTR BY RAISING GEAR; FLAPS; SETTING MCP FOR CLB MODE; SETTING HDG AND DOING RADIO WORK. AUTOMATION: FLT DIRECTOR 'THOUGHT' IT SHOULD TURN R BECAUSE THAT WAS THE SHORTEST WAY TO GET TO DESIRED HDG.