A B737-300 FLC TURNS THE WRONG DIRECTION WHEN THE PIC; PF; MISREADS THE SID CHART SE OF DAL; TX.

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THERE WERE TSTMS ALL AROUND THE DALLAS/FORT WORTH AREA WITH MORE INTENSE WX TO THE W OF DALLAS. MY FO INFORMED ME THAT THERE WAS A BACK UP ON CLRNC AND THAT WE WERE #3 AND TO EXPECT A RERTE TO THE N. THE OPS AGENT ARRIVED WITH THE LOAD SHEET AND CLOSED THE MAIN CABIN DOOR AT THE SAME TIME THE CLRNC CAME THROUGH. WE PUSHED FROM THE GATE AND TAXIED TO RWY 13R. AT THE COMPLETION OF THE PRETKOF CHKLIST; THE FO AND I DISCUSSED THE RERTE. THIS ENTAILED FLYING N ON THE TEXOMA 7 DEP WITH THE IRW TRANSITION. WE WERE STOPPED AT THE RWY END AND I PULLED THE SID AND STARTED TO REVIEW THE PROC. BUT I WAS CONCERNED WITH THE ADDITIONAL FUEL BURN AND PUT IN A CALL TO DISPATCH. WE INITIALLY HAD AN ALTERNATE OF ABQ AND AN ADDITIONAL FUEL BURN CALCULATION OF 3800 LBS BECAUSE OF THE RERTE. DISPATCH CAME ON IMMEDIATELY AND AFTER A SHORT DISCUSSION; WE CAME TO THE CONSENSUS THAT AMA COULD SERVE BEST AS OUR NEW ALTERNATE BECAUSE OF A MUCH LESS ALTERNATE FUEL BURN. THIS WOULD PERMIT US TO LEAVE WITH FUEL ON BOARD. THE TWR CALLED OUR FLT GIVING US CLRNC FOR IMMEDIATE TKOF; AS THERE WAS COMPANY TFC ON A 3 MI FINAL. I GLANCED QUICKLY AGAIN AT THE SID AND MY EYES FOCUSED ON THE PROC FOR RWY 31L/R INSTEAD OF RWY 13L/R WHICH REQUIRED A R TURN AT 5.5 DME. THE WX RADAR WAS OPERATING ON THE TKOF ROLL WITH A NUMBER OF CELLS 6-8 MI OFF THE END OF THE RWY. A NORMAL TKOF AND CLB THROUGH 1000 FT WAS EXECUTED. WE CONTACTED DEP AND WERE CLRED TO 8000 FT. AT 5.5 DME I INITIATED A R 30 DEG BANK TURN TOWARD 360 DEGS. I TURNED WITH HASTE BECAUSE OF WX AT 12-1 O'CLOCK POS THAT I WANTED TO GET INSIDE OF. AT THIS POINT; MY FO AND I ASKED THE SAME QUESTION -- 'WHY ARE WE TURNING TO THE R?' I IMMEDIATELY STOPPED THE TURN WHEN I REALIZED THAT A RWY HDG WAS TO BE MAINTAINED; AND CAME BACK TO THE L AROUND THE CELL WITHOUT HESITATION. AS WE WERE ALMOST BACK TO RWY HDG; THE CTLR DIRECTED US L TO A HDG OF 350 DEGS. IN THE SAME BREATH HE ASKED; 'WHAT ARE YOU GUYS DOING?' WE IMMEDIATELY APOLOGIZED FOR THE DEV AND ADVISED HIM OF THE WX AVOIDANCE. HE WAS EXTREMELY AGITATED AND TOLD US THAT HE SHOULD CLR ANY DEV FOR WX FIRST. WE AGAIN APOLOGIZED. UPON THE TURN WE WERE ABLE TO AVOID THE CELL; WHICH WAS DIRECTLY IN OUR PATH ANYWAY AND WAS A CONTRIBUTING FACTOR IN REINFORCING MY THINKING THAT A R TURN ON THE SID WAS GOING TO HELP ME AVOID THE WX. THE REMAINDER OF THE FLT WAS UNEVENTFUL. I CAN ONLY SURMISE THAT THE CHANGING FLT PLAN; FUEL CONSIDERATIONS; WX AND THE EXPEDITIOUS MANNER IN WHICH WE DEPARTED DALLAS CONTRIBUTED TO MY MENTAL ERRORS.