ARR ACR MLG GETS MANY HDG AND ALT CHANGES WHILE BEING VECTORED FOR AN APCH TO RWY 26 AT IAH; TX. TCASII RA ALERTS CREWS OF DEP AND ARR TFC THAT SOMETHING IS NOT RIGHT. THEY STOP THEIR CLB AND DSCNT FOR TFC AVOIDANCE.

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DURING APCH FOR IAH RWY 26 ESTABLISHED ON LOC AT 4000 FT. CTLR CLRED US; ACR X; FOR APCH. OM ON GS IS 2000 FT. WE WERE LESS THAN 1 MI FROM OM. WE DECLARED UNABLE TO DO APCH. WE WERE GIVEN A TURN AND A CLB; THEN A FURTHER TURN AND A DSCNT. WE THEN RECEIVED A TCASII WARNING AND LEVELED. WE NEVER SAW OTHER ACFT. SUPPLEMENTAL INFO FROM ACN 362862: HE THEN GAVE US A TURN OFF COURSE TO 360 DEGS AND DSND TO 2000 FT. HE THEN CAME BACK; ASKED OUR ALT (3300 FT) AND ASKED US TO MAINTAIN THAT ALT. HE THEN HAD US TURN R TO 090 DEGS AND CLB TO 4000 FT THEN AGAIN DSND TO 2000 FT. WE SUCCESSFULLY COMPLETED THE APCH. I SPOKE WITH THE TRACON SUPVR SHORTLY THEREAFTER AND FOUND THAT THE CTLR WAS IN A TRAINING SIT. HE KEPT US HIGH ANTICIPATING A VISUAL APCH SLOT FOLLOWING 2 ACFT ON RWY 27. WHEN HE TURNED US OFF COURSE WE NOW HAD A POTENTIAL CONFLICT WITH A RWY 14L DEP TURNING NBOUND AND CLBING TO 4000 FT. THAT TFC STOPPED AT 2500 FT OR SO; AND OUR DSCNT STOPPED AT 3300-3500 FT. THE OTHER ACFT DID HAVE A TCASII RA AT THE TIME AND STOPPED HIS CLB. IN RETROSPECT; MY FO ADVISED ME THAT WE HAD A TCASII RA AS WELL; BUT HAD ALREADY STOPPED OUR DSCNT.