ACR X NON ADHERENCE TO ATC CLRNC STOPPED DSCNT DUE TO TCASII TA WHICH TURNED INTO A TCASII RA. PLT DEV.

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ACR X DURING DSCNT THE CENTER CTLR GAVE US A LATE XING RESTRICTION TO CROSS 40 NM NW OF HOBBY AT 10M. WE WERE NAVIGATING AROUND TSTMS AND WERE HDG APPROX 060 DEGS. CENTER HAD ASKED US TO ADVISE WHEN WE WOULD BE ABLE TO TURN TO A HDG OF 100 DEGS TOWARD HOBBY AND HAD GIVEN US THE HUMBLE ALTIMETER SETTING. I ADVISED THAT WE WERE NOT GOING TO HUMBLE; BUT HOBBY. CENTER SAID THE ALTIMETER SETTING WAS THE SAME. I THEN NOTICED AN INTRUDER ON OUR TCASII RAPIDLY APCHING AT 12 O'CLOCK; BUT VISUALLY I COULD SEE NOTHING OUT THE WINDOW. THE ALT OF THE INTRUDER INDICATED THAT A PROBABLE CONFLICT WOULD OCCUR IF WE CONTINUED OUR DSCNT. I ADVISED HOUSTON CENTER THAT WE COULD NOT MAKE THE XING RESTRICTION DUE TO TCASII CONFLICT AND RECEIVED NO REPLY. 2 TRANSMISSIONS WERE MADE WITH NO REPLY. THE TCASII THEN ANNOUNCED 'TFC; TFC' THEN 'DSND; DSND' FOLLOWED BY 'CLB; CLB.' THE ACFT WAS LEVELLED AT APPROX 13800 FT IN A SLIGHT CLB. TCASII INDICATIONS SHOWED THE INTRUDER PASSING OFF TO THE L. WE WERE THEN HANDED OFF TO A LADY CTLR WHO GAVE US A VECTOR HDG FOR A LNDG ON RWY 14L. I RESPONDED THAT WE WERE GOING TO HOBBY AND THAT THERE WAS NOT A RWY 14 AT THAT ARPT. SHE SAID TO DISREGARD. THIS WAS THE SECOND OCCURRENCE OF VECTORS TO THE WRONG ARPT WITHIN THE PREVIOUS 30 DAYS. ONCE ON THE GND I COMMUNICATED WITH 2 DIFFERENT SECTIONS OF HOUSTON CENTER; THE LATTER CORPUS CHRISTI; AND ADVISED REGARDING THE TCASII RA (RESOLUTION ADVISORY).