RPTR'S ACFT X LOST STANDARD SEPARATION WITH ACFT Y WHILE THEY WERE AVOIDING WX.

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WE WERE INITIALLY GIVEN A 070 DEG HDG FROM DEP CTL FOR WX AVOIDANCE. OUR SID SHOULD HAVE BEEN A 190 DEG HDG. THE 070 DEG HDG WOULD MAKE US FLY RIGHT THROUGH A LEVEL 4 TSTM. WE REQUESTED A L DEV. DEP SAID THAT CTR WAS NOT ALLOWING ANY L DEVS. DEP THEN OFFERED A R TURN DIRECT TO TFD (STANFIELD) VOR WHICH WAS ON OUR ORIGINAL PUSCH SID. WE ACCEPTED THE OFFER AND TURNED R; TOWARD THE TFD VOR. AS WE WERE TURNING THROUGH 150 DEGS TOWARDS THE VOR; DEP THEN TOLD US THAT CTR WAS NOT ACCEPTING ANY ACFT OVER TFD AND SAID THAT THEY WOULD NOW ALLOW L DEVS IF WE COULD TURN BACK L TO THE N. WE BEGAN OUR L TURN TO AN ASSIGNED HDG OF 030 DEGS. DEP TOLD US TO CONTACT CTR. WE WERE NOW FLYING THROUGH THE FRINGES OF THE TSTM IN RAIN; TURB AND CLOUDS. WE CHKED IN WITH CTR ON A 030 DEG HDG. IT WAS APPARENT THAT WE WOULD NEED A TURN TO THE L TO ABOUT A 010 DEG HDG IN A FEW MI TO AVOID WX. THE FO WAS FLYING. I TOLD THE FO I WOULD BE OFF THE RADIO WITH CTR SO I COULD RELAY THE 'OFF' TIMES TO OPS. SHE SAID 'OK.' WHEN I RETURNED BACK TO THE FREQ; WE WERE ON A 010 DEG HDG. THE FO LATER TOLD ME THAT SHE HAD TOLD CTR THAT SHE NEEDED A L DEV FOR A LITTLE BIT AND CTR CLRED HER TO DEVIATE TO 010 DEGS. CLBING THROUGH 15000 FT; I NOTICED SOME TFC DISPLAYED ON THE TCASII AT OUR 10 O'CLOCK POS AND 5 MI THAT WAS 500 FT BELOW US. I TOLD THE FO TO INCREASE OUR CLB TO AVOID AN RA. SHE HAD TROUBLE WITH THE AUTOMATION AND SO THE INCREASE IN CLB WAS DELAYED. JUST AS WE WERE INCREASING OUR CLB; CTR TOLD US TO INCREASE OUR RATE OF CLB THROUGH 16000 FT. WE DID; BUT THE OTHER ACFT (ACFT Y) CAME WITHIN 3 MI AND 500 FT. CTR NEVER GAVE ANY INDICATION THERE WAS A PROB UNTIL THEY TOLD US TO CALL WHEN WE WERE FLYING OVER ELP. CTR COULD HAVE PREVENTED THE PROB BY VECTORING US OR THE OTHER ACFT AWAY. AFTER WE SPOKE WITH THE ATC MGR; HE SAID IT LOOKED LIKE IT WAS THE CTLR'S FAULT. I CONCUR!