B737 DEPARTING AGS PENETRATES MOA; MISSES TURN ON AIRWAY WITH TCASII TA.

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THE INITIAL PART OF OUR CLRNC WAS TO FLY THE AGS 1 -- DUBLIN TNS. ON THE CLBOUT; WE WERE GIVEN AN INITIAL HDG OF 270 DEG. AFTER FLYING THAT FOR SEVERAL MINS; I ASKED FOR A SOUTHERLY TURN. DEP SAID THAT WE COULD REQUEST THIS FROM ZTL WHEN WE SWITCHED OVER; HE STATED THAT WE WERE GIVEN THE AGS 1. THE INITIAL PART OF THE TRANSITION HAS A 199 DEGS R INTERCEPT OFF OF COLLIERS VOR; WHICH WE PROCEEDED TO FLY. WE WERE SWITCHED OVER TO ZTL AND A COUPLE OF MINS; ATC SAID WE HAD FLOWN INTO AN ACTIVE MOA. HE ASKED WHY WE HAD TURNED FROM 270 DEG HDG. WE SAID IT WAS OUR UNDERSTANDING THAT WE WERE EXPECTED TO FLY THE AGS -- (DUBLIN TNS). THEY TURNED US BACK TO 270 DEG HDG; AND WE FLEW OUT OF THE MOA. AS FAR AS THE 270 DEG HDG AND OUR INTERCEPT OF THE 199 DEG. R; I STILL FEEL THAT IT WAS AN AMBIGUOUS SIT; WHICH I DIDN'T QUESTION AT THE TIME; BECAUSE I THOUGHT WE AND ATC WERE ON THE SAME PAGE. SHORTLY AFTER WE GOT OUT OF THE MOA; ZTL GAVE US A CHANGE TO OUR RTING. WE WERE CLRED TO DUBLIN VOR; DIRECT CRAIG; J-45; ORM; SFD. WE WERE CLOSE TO THE DUBLIN VOR; ACTUALLY JUST PASSING OVER; WHEN I VERIFIED WITH THE FO; WHO WAS FLYING; THAT CRAIG WAS 114.5. HE STARTED A L TURN; AND I PICKED UP THE CHART TO CHK J-45. AFTER A LITTLE BIT; I REALIZED WE STARTED A TURN BACK TO THE R. I QUERIED HIM ON WHAT HE WAS DOING; AND STATED THAT CRAIG WAS 160 DEG HDG. HE HAD TURNED 40-50 DEGS; PASSED THROUGH THE L INITIALLY. HE TOLD ME HE HAD ACCIDENTALLY SET IN 113.5. AS HE WAS TURNING BACK TO THE R TO CORRECT; I SAW A TA COME UP ON THE TCASII. IT WAS APPROX 800 FT BELOW US; AND WE CLBED 200 FT ABOVE OUR CRUISING ALT OF FL230. THE TA WENT AWAY; BUT ABOUT THAT TIME; ATC ASKED US WHERE WE WERE GOING. WE WERE ROLLED OUT ON THE PROPER 160 DEG HDG FOR CRAIG BY THAT TIME; WHICH IS WHAT I READBACK. THERE WAS NO FURTHER COMMENT FROM ATC AND BELIEVE IT OR NOT; WE PROCEEDED TO OUR DEST WITHOUT ANY ADDITIONAL PROBS. ON THE GND; I RECEIVED A REQUEST TO CALL ZTL SUPVR. WE BASICALLY DISCUSSED EVERYTHING. WE HAD A CONSTRUCTIVE DISCUSSION AND I GOT THE IMPRESSION THAT HE WAS NOT GOING TO GO ANY FARTHER WITH THIS. MY COMMENT ABOUT THIS SECOND PROB IS THIS: I HOLD MYSELF TOTALLY RESPONSIBLE AND SHOULD HAVE FOUND A WAY TO HAVE AVOIDED THE WHOLE INCIDENT. IT REALLY BOTHERS ME THAT OUR COCKPITS ARE ALL SET UP DIFFERENTLY. SOME HAVE SUBTLE DIFFERENCES; WHILE OTHERS HAVE VERY BIG DIFFERENCES. I HAVE VOICED MY DISAPPROVAL OF THE SIT. I REALIZE THIS DOES NOT LEAVE ME OFF THE HOOK FOR WHAT TRANSPIRED; BUT I DID HAVE A THOROUGH DISCUSSION WITH MY FO ABOUT HOW WE COULD HAVE AVOIDED GETTING INTO ANOTHER SIT LIKE THIS. I FOUND OUT LATER THAT THE FO HAD COMMUTED IN FROM THE WEST COAST JUST IN TIME TO CREW THIS FLT. HE SAID HE WAS TIRED; WHICH I HADN'T KNOWN -- I TOLD HIM THAT THIS WAS UNACCEPTABLE.