AFTER A HARROWING FLT THROUGH A THUNDERSTORM AND POOR FLT HANDLING; A HS125 FLT CREW CALLS THE ABQ ARTCC SUPVR AFTER LNDG SAN AND ARE ASKED IF THE FLIGHT CREW WAS ON DRUGS.

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DEPARTED KDAL XA30 ZULU ENRTE TO KSAN. WE WERE CLRED TO FL350 FOR THE ENRTE CRUISE PORTION OF THE FLT. AFTER PASSING TXO-VOR WE WERE CLRED DIRECT TO THE GBN-VOR. ZAB HAD TAKEN CTL AT THIS TIME. ZAB ATC ASKED IF WE COULD ACCEPT FL390. THE CAPT (PIC) SAID THAT WE COULD BUT IT WOULD TAKE A WHILE TO REACH FL390. IT TOOK ABOUT 12 MIN TO REACH FL390. THERE WAS A LINE OF SEVERE WX FROM W OF EL PASO TX/NM/CO TOPS ABOVE FL450. MOST ALL ACFT WERE DEVIATING FOR THIS WX. OUR ACFT TRACK AND ALT WAS OK TO PASS BTWN AND OVER THE WORST BUILD-UPS. ZAB ATC ASKED IF WE COULD TURN L (S) FOR A VECTOR. THIS VECTOR WOULD HAVE TAKEN US DIRECTLY INTO WX S OF OUR POS. THE PIC INSTRUCTED ME (SIC) TO TELL ATC THAT WE COULD ONLY GO STRAIGHT AHEAD BECAUSE OF THE WX S; N; AND BELOW US AT THIS TIME. ZAB ATC THEN TOLD US TO DSND TO FL350. I REPEATED THE CLRNC BACK. THE PIC INSTRUCTED ME TO INFORM ATC THAT WE WERE GOING DOWN INTO THE WX BELOW US. ABOUT FL38.5 WE ENCOUNTERED STRONG UPDRAFTS WHICH SET OFF OUR MM OVERSPEED HORN. THE OVS BREAKER WAS PULLED TO KEEP OUR PAXS CALM WHILE WE TRIED TO DSND. ZAB ATC STARTED CALLING WANTING TO KNOW WHY WE WERE NOT COMING DOWN FAST ENOUGH TO SUIT THEM. THE PIC TOLD ZAB ATC (HIMSELF) THAT HE WAS DOING THE BEST HE COULD. HE DID THIS 3 TIMES WHILE FLYING AS WELL AND THAT WE WERE ABOUT TO LOSE OUR CAB PRESSURATION AS WELL. ATC SAID SOMETHING ABOUT 16 DEGS LEFT. THE FLT DECK NOISE LEVEL WAS VERY HIGH DUE TO THE RADIO STATIC; ACFT SPEED; WX/ICE. I RPTED THROUGH FL370 TO ZAB ATC 2 OR 3 TIMES. FINALLY ZAB ATC WAS HEARING AND TOLD US TO TURN L 60 DEG AND GET DOWN TO FL350 OR WE WOULD BE MEETING A B777. ABOUT 1 MIN LATER WE POPPED OUT OF THE W SIDE OF THE THUNDER STORM. ZAB ATC THEN SWITCH US TO ANOTHER ZAB ATC FREQ. THE PIC ASKED THIS CTLR WHAT WAS THE PROB. WE WERE TOLD TO CALL THEM ON THE LANDLINE TO GET THE ANSWER. THE REST OF THE FLT WAS UNEVENTFUL. AFTER LNDG IN KSAN I (SIC) CALLED ZAB BECAUSE THE (PIC) WAS STILL UPSET OVER OUR FLT HANDLING BY ZAB. I ASKED FOR THE SUPERVISOR AND SOME PERSON GOT ON THE PHONE AND WANTED TO KNOW IF WE WERE ON DRUGS? I TOLD THIS PERSON IF THIS WAS IN QUESTION THAT WE WOULD RPT TO THE TWR IN KSAN AND THAT THEY SHOULD DO THE SAME. I TURNED THE PHONE OVER TO THE PIC WHICH EXCHANGED A FEW WORDS WITH THE ZAB SUPVR.