C172 MAKES WRONG RWY APCH WITH C210 DEPARTING. DWH E CTLR ALERTS W CTLR TO ABORT C210 TKOF.

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THIS ARPT HAS PARALLEL RWYS. SOMETIMES; LCL CTL IS SPLIT BTWN 2 LCL CTLRS -- ONE FOR THE W RWY AND ONE FOR THE E RWY. THE LCLS WERE SPLIT WHEN THE SKYHAWK RPTED INBOUND FROM THE W FOR TOUCH-AND-GO OPS. TOUCH-AND-GO OPS ARE USUALLY CONDUCTED ON THE E RWY WHERE I WAS THE CTLR (RWY 17L). I COORDINATED WITH THE OTHER LCL CTLR (RWY 17R) TO HAVE THE SKYHAWK PLT CONTACT ME ON A 3 MI R BASE; SO I COULD INTEGRATE HIM INTO THE PATTERN WITH ANOTHER SKYHAWK ON L DOWNWIND. ON INITIAL CONTACT; I INSTRUCTED THE R BASE SKYHAWK TO RPT THE DOWNWIND SKYHAWK IN SIGHT. HE RPTED HIM IN SIGHT AND I TOLD HIM HE WAS TO FOLLOW THE ACFT AND CLRED HIM FOR TOUCH-AND-GO ON RWY 17L. HE READ BACK 'CLRED ON THE R;' WHICH I DID NOT CATCH. THE LCL W CTLR PUT A CENTURION IN POS AND HOLD AS THE SECOND SKYHAWK TURNED TO FINAL. THE SKYHAWK LINED UP ON RWY 17R AND I TOLD HIM TO GO AROUND ABOUT 1/8 MI SHORT OF THE THRESHOLD. HE DIDN'T RESPOND AND THE LCL W CTLR CLRED THE CENTURION JUST AS THE SKYHAWK PASSED ABOUT 30 FT OVERHEAD. I YELLED AT THE LCL W CTLR TO ABORT THE CENTURION'S TKOF; THEN TOLD THE SKYHAWK PLT TO GAR AGAIN; WHICH HE DID. CLOSEST PROX WAS 30 FT DIRECTLY OVERHEAD. THE SKYHAWK RE-ENTERED THE PATTERN AND MADE A NORMAL LNDG. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: FACILITY SPECIALIST ADVISED THAT DWH HAS LIMITED APCH CTL AUTH; BEING ABLE TO PROVIDE SEPARATION BTWN ARRS AND DEPS.