ATR72 FLC DEVIATING WX HAS ALTDEV AND LITTLE ATC ASSISTANCE.

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APCHING HOU FROM DFW; WE WERE VECTORED SW OF HOU BTWN 2 LARGE TSTMS FOR AN APCH TO RWY 4. THE TSTMS WERE MOVING W TO E WHICH SUGGESTED TO ME THAT THE STORM TO MY R WAS MOVING ACROSS OUR RTE OF FLT AS WE MOVED S. AS WE STARTED THE INTERCEPT TO THE ILS COURSE FOR RWY 4; THE APCH CTLR INFORMED US THAT THE STORMS HAD MOVED ACROSS THE FIELD; RWY 4 WAS CLOSED; AND WE WERE GOING TO BE VECTORED TO RWY 12. HE TOLD US TO MAKE A TURN N INTO THE TSTM ON MY W SIDE. AT THIS POINT; I FELT THAT I WAS IN A 'BOX CANYON' OF TSTMS. WE WERE NOW EXPERIENCING CONTINUOUS MODERATE TURB. I COULD SEE THAT TO THE S AND ONLY A FEW MI AWAY THAT THERE WERE CLR SKIES; DETERMINED BY LOOKING AT SUNLIGHT BELOW BASE OF CLOUDS. WE REQUESTED A HEADING OF S TO AVOID AREA OF TSTMS AND TURB. WHEN WE DSNDED TO 2700 FT MSL; APCH CALLED US SEVERAL TIMES TO TELL US TO MAINTAIN 3000 FT. ALTHOUGH I ADJUSTED THE NOSE ATTITUDE TO 5 DEGS ABOVE THE HORIZON; WE CONTINUED TO HAVE DIFFICULTY MAINTAINING AN ALT OF 2700 FT. I THINK THAT I MADE A MISTAKE BY FAILING TO INFORM THE CTLR THAT WE WERE IN AREA OF CONTINUOUS; MODERATE TURB. I COULD TELL BY THE RADIO XMISSIONS THAT THE CTLR WAS BUSY VECTORING OTHER TFC. WE REQUESTED A DSCNT TO 2000 FT DUE TO WX; THE CTLR TOLD US THAT HE WAS UNABLE TO GIVE IT TO US. IN A FEW MINS; WE ENTERED AN AREA OF CLR SKIES AND SMOOTH AIR. VISIBILITY WAS BETTER THAN 10 MI AND WE COULD SEE THAT THERE WERE NO CLOUDS S OF THE LINE OF TSTMS. WE REQUESTED HOLDING AND WERE GIVEN A HEADING OF SE FOR GALVESTON. HOWEVER; THE CTLR THEN INFORMED US THAT THE STORMS WERE MOVING OVER GALVESTON AND TURNED US TO A HEADING OF N 360 DEGS. THIS NEW HEADING WAS TAKING US RIGHT BACK INTO THE AREA OF TURB AND TSTMS THAT WE HAD RECENTLY PASSED THROUGH. AS WE HEADED N; WE REQUESTED A TURN W FOR WX. EACH TIME WE MADE THIS REQUEST; WE WERE TOLD TO 'STANDBY.' I MAINTAINED A N HEADING UNTIL IT APPEARED TO ME THAT WE WERE GOING TO RE-ENTER AN AREA OF TURB. I THEN TURNED TO THE W HEADING 240 DEGS. THIS WAS AN AREA OF CLR SKIES. THE FO INFORMED CTR THAT WE WERE GOING W-SW. WE REQUESTED HOLDING AT PALACIOS WHICH WE WERE APCHING. THIS WAS AN AREA OF CLR SKIES AND SMOOTH AIR. INSTEAD; THE CTLR GAVE US A VECTOR TO EAGLE LAKE. AS OUR RADAR SHOWED TSTMS AT EAGLE LAKE; AND OTHER ACFT WERE RPTING TSTMS AT EAGLE LAKE; WE REQUESTED A DIFFERENT HOLDING POINT. THE CTLR TOLD US THAT HE WOULD TURN US BEFORE EAGLE LAKE AND SET US UP FOR AN APCH TO RWY 12 AT HOUSTON. FOLLOWING THE VECTORS ASSIGNED; WE WERE SET UP FOR THE ILS RWY 12 AT HOUSTON. SINCE MY RADAR INDICATED A TSTM AT THE ARPT; I ASKED APCH WHERE IT WAS. HE TOLD ME THAT IT WAS 4 MI S OF THE ARPT. AT THIS POINT; I DECIDED TO DIVERT TO COLLEGE STATION. THE CTLR ONLY APPROVED 1 HEADING CHANGE AT THE TIME I REQUESTED IT. I BELIEVE THAT THE ATC CTLR WAS RUSHING ME FOR HIS REASONS AND IGNORED MY REQUESTS FOR HOLDING. I WANTED TIME TO ANALYZE THE SIT AND CONSIDER AN APPROPRIATE COURSE OF ACTION.