FLC RPTS UNINTENDED TURN ON AUTOPLT DURING DIRECT CLRNC.

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DEPARTING DALLAS-FORT WORTH (DFW) ENRTE VIA A DIRECT ROUTING TO SAN ANTONIO (SAT); WE WERE ADVISED TO EXPECT A REVISED RTE DUE TO WX IMPACTING DEP AIRSPACE. INITIAL RERTE WAS TO INTERCEPT AND PROCEED OUTBOUND ON DFW 253 DEG RADIAL WITH FULL CLRNC TO FOLLOW. AFTER INTERCEPTING AND TRACKING OUT THE DFW 253 DEG; REVISED RTE WAS ISSUED DIRECT ABILENE (ABI) DIRECT SAN ANGELO; DIRECT SAN ANTONIO. DIRECT ABI WAS ENTERED INTO FMS (AREA NAV). CLB CLRNC FROM 17000 FT TO FL230 WAS RECEIVED FOLLOWED BY CLRNC TO FL310. WHILE LOOKING UP IDENT FOR SAN ANGELO TO INPUT FMS AND KEEPING WATCH ON WX OFF OUR RTE DIRECT ABI; ACFT BEGAN SLOW TURN TO THE R. SHORTLY AFTERWARDS; THIS TURN WAS DISCOVERED AND AN IMMEDIATE L TURN BACK TO DIRECT ABI WAS STARTED. ZFW CALLED FOR IMMEDIATE L TURN TO A HDG L OF DIRECT ABI AND REQUESTED AN EXPEDITED CLB A FEW MOMENTS LATER. SOME CONFUSION OVER WHO WAS TO EXPEDITE CLB/STOP CLB RESULTED FROM BLOCKED/CLIPPED RADIO CALLS BTWN ATC AND OTHER ACFT. AM UNSURE IF SEPARATION WAS DEGRADED OR NOT; BUT NO OTHER ACFT WERE OBSERVED IN OUR IMMEDIATE VICINITY ON TCASII. I BELIEVE THIS INCIDENT RESULTED FROM A COMBINATION OF CONCERN WITH WX; REVISED CLRNC; AND INITIAL DIFFICULTY WITH FMS ACCEPTING THE REVISED ROUTING INPUTS THAT I WAS MAKING. PNF WAS ATTEMPTING TO HELP XCHK THE NAV INPUTS TO THE FMS THAT I WAS MAKING AND THE TURN OFF COURSE (DIRECT ABI) BY THE AUTOPLT WAS NOT IMMEDIATELY DISCOVERED BECAUSE OF TURB AND IMC CONDITIONS. OTHER FACTORS INVOLVED FATIGUE RESULTING FROM DEALING WITH WX DELAYS ON PREVIOUS FLTS AND BELIEVING YOU SEE WHAT YOU EXPECT TO SEE DISPLAYED ON COCKPIT NAV ANNUNCIATIONS.