CL65 CAPT TURNS FROM COURSE TO DIVERT PRIOR TO ADVISING ATC OF NEED FOR A NEW CLRNC FOR DIVERTING RESULTING IN A CONFLICT ALERT WITH ANOTHER ACFT.

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SCHEDULED PAX PART 121 FLT ELP-DFW; DIVERTED TO TXK DUE TO POP-UP TSTMS OVER DFW; AND INSUFFICIENT FUEL TO HOLD. VERY BUSY COORDINATING WITH ATC AND DISPATCH. HAD JUST BEEN GIVEN DSCNT FROM FL240 WHEN DISPATCH ADVISED US IN A NEW RADIO CONTACT TO DIVERT TO SHV INSTEAD; DUE TO A LACK OF SECURITY PERSONNEL AT TXK. CAPT WAS TALKING TO DISPATCH WHILE I TALKED TO ATC; EVEN THOUGH HE WAS PF. HE NEVER INSTRUCTED ME TO TAKE CTLS. IN HINDSIGHT; I SHOULD HAVE INSISTED. VERY CONFUSING 2-4 MINS DUE TO DISPATCH FREQ FADING AND OUR HAVING TO RE-ESTABLISH CONTACT ON NEW FREQ; WITH A LACK OF INITIAL INFO OTHER THAN 'DIVERT.' I TOLD ATC WE DIDN'T WANT TO DSND YET AS WE MIGHT BE GOING SOMEWHERE ELSE; SO WE MAINTAINED FL240 AND COURSE TO TXK. CAPT WAS ANGRY AT OVERALL SIT AND UNWILLING TO CHANGE DEST INITIALLY; THEN ABRUPTLY TURNED ACFT 90 DEGS R TOWARDS SHV WITHOUT EXPLAINING TO ME; OR ADVISING ATC. WHEN I FOUND OUT WE WERE NOW GOING TO SHV; I INFORMED ATC OF OUR NEW HDG TO GET DSCNT CLRNC. CORRECTION: I TOLD ATC WE NEEDED TO GO TO SHV; ATC GAVE US 'DSND TO FL180.' I THEN TOLD HIM OUR NEW HDG. ATC REPLIED WE HAD 'TURNED IN A CONFLICT WITH ANOTHER ACFT; EXPEDITE DSCNT THROUGH FL180; DSND TO 15000 FT.' WE COMPLIED. REST OF TRIP UNEVENTFUL. (DFW CTL TWRS AND TERMINALS LATER EVACED DUE TO TORNADOES.)