FLC OF MLG ACR ACFT DEVIATED FROM ASSIGNED TRACK AND DECLARED A WX EMER. POTENTIAL CONFLICT LTSS.

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SIGMET 2-34 151-55 31E AND VISUAL SIGHTINGS INDICATED STRONG TSTMS IN AREA. WHEN CLRED INTO POS WE TURNED ON THE RADAR AND THE RADAR PRESENTATION INDICATED A LINE OF VERY INTENSE CELLS FROM A FEW MI SW OF RWY 19L AT IAD STRETCHING S AND SLIGHTLY W FOR AN UNDETERMINED DISTANCE. WE ASKED FOR AND RECEIVED A HDG OF 170 DEGS AFTER TKOF TO AVOID THESE BUILD-UPS. DURING OUR TKOF ROLL; I OVERHEARD TWR ADVISE THE ACFT BEHIND US THAT 'THEY' HAD SHUT OFF DEPS. WE WERE HANDED OFF TO DEP. THEY ASKED IF WE COULD TURN R AND WE SAID WE WERE UNABLE DUE TO WX. WE WERE PASSED OVER TO APCH CTL SOMEWHERE AFTER REACHING 14000. WE WERE GIVEN A CLB TO (I THINK) 21000 AND AGAIN ASKED TO TURN R TO A HDG OF 220 DEGS. WE SAID UNABLE DUE WX. CTLR SAID TO LEVEL AT 19000 AND EITHER TURN R TO 220 DEGS OR DECLARE A WX EMER. I TOLD THE FO TO SAY WE COULD GO TO 195 DEGS BUT NO FARTHER. HE TOLD US TO LEVEL AT 18000 AND TURN R IMMEDIATELY TO 270 DEGS OR DECLARE WX EMER. I THOUGHT I SAW A SMALL HOLE AND STARTED TURN; BUT THIS DISAPPEARED INTO SOLID RED AREA WITH VERY STEEP GRADIENT. I LEVELED WINGS AND TOLD FO TO DECLARE A WX EMER. FIRST XMISSION WAS BLOCKED BUT SECOND XMISSION GOT THROUGH. ABOUT THIS TIME WE RECEIVED A TA. TFC APPEARED ON SCOPE AND AN RA CAME UP; BUT BEFORE I COULD RESPOND WE HAD A 'CLR OF TFC' ON TCASII. SOON AFTER WE WERE TOLD TO SWITCH FREQS. THIS WAS THE ROCK AND THE HARD PLACE SCENARIO. THE TIME FRAME SEEMED VERY SHORT -- 45 SECONDS TO A MIN -- BUT MAY HAVE BEEN LONGER. I FEEL THAT; DUE TO THE SEGMENTED STRUCTURE OF CTL; WE WERE GIVEN THE IMPRESSION WE COULD AVOID THIS VERY HAZARDOUS WX; AND THEN TOLD TO FLY THROUGH IT. THE CTLR; IT APPEARED; WAS GIVEN A SIT WITH VERY LITTLE MANEUVERING SPACE AND LITTLE TIME TO DEAL WITH IT. WE WERE PRESENTED WITH 2 CHOICES; BOTH HAZARDOUS; AND WITH EVEN LESS TIME TO DECIDE. WITH FAST MOVING HAZARDOUS WX AND HIGH TFC VOLUME; KEEP THE ACFT ON THE GND. HAD I KNOWN AHEAD OF TIME THE RESTRICTIONS THAT WOULD BE PLACED ON US; I WOULD; OF COURSE; HAVE TAKEN OTHER ACTIONS. SUPPLEMENTAL INFO FROM ACN 239214: WE AGAIN REPEATED THAT WE WERE DECLARING A WX EMER AT WHICH TIME THE CTLR SAID MAINTAIN A HDG OF 195 DEGS (WHICH WE WERE NOW ON) AND MAINTAIN FL180. WE WERE THEN ISSUED TFC AT 11-12 O'CLOCK DSNDING OUT OF FL190 FOR FL180 ON 170 (I'M NOT QUITE SURE OF THESE ALTS). THE CTLR CONTINUED TO ISSUE THIS TFC WITH A VERY ALARMED AND EXCITED MANNER. WE THEN PICKED UP THIS TFC ON TCASII WITH A TA FOLLOWED BY A CLB COMMAND AND THEN FOLLOWED BY CLR OF TFC. WE WERE IN IMC CONDITIONS BUT JUDGING FROM THE TCASII DISPLAY; THIS TFC PASSED OFF TO OUR L 2-3 MI AT ALMOST THE SAME ALT.