D10 CTLR EXPERIENCED OPERROR AT 2500 ATTEMPTING TO VECTOR GKY DEP AWAY FROM DFW ARR BEING VECTORED OFF FINAL BECAUSE OF AN EMER ACFT.

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I WAS WORKING MEACHAM S SECTOR AT DFW TRACON. THE BE65 WAS AN IFR DEP OFF GKY ARPT THAT UNDERLIES RWY 36L FINAL FOR DFW ARPT AND IS IN ARR 3 AIRSPACE. DFW PROCS REQUIRE GKY TWR TO COORDINATE A DEP WITH MEACHAM S. MEACHAM S IS THEN REQUIRED TO COORDINATE WITH ARR 3 AND THEN CALL GKY TWR BACK WITH THE IFR RELEASE. I COORDINATED THE BE65 DEP WITH ARR 3; HDG 320 DEGS CLBING TO 2000 FT. TRAINING WAS IN PROGRESS ON ARR 3. AFTER THE BE65 WAS AIRBORNE OFF GKY I INITIATED AN AUTOMATED POINTOUT TO ARR 3 AND CALLED ARR 3 ON THE LAND LINE TO COORDINATE A TURN AND HIGHER ALT. THE MVA TO THE W OF THE 320 DEG HDG IS 2700 FT. WHEN I ACTIVATED THE OVERRIDE FUNCTION TO ARR 3; I OVERHEARD THE OJT INSTRUCTOR TELL THE SUPVR AN ARR HAD JUST DECLARED A MEDICAL EMER. I ALSO HEARD THE DEVELOPMENTAL TURN THE E145 TO A 330 DEG HDG OFF THE RWY 36L FINAL. I CAME OFF THE OVERRIDE AND 'QUICK LOOKED' ARR 3 TFC. IN AN ATTEMPT TO VECTOR THE BE65 AWAY FROM THE MEDICAL EMER INBOUND AND THE E145 BEING VECTORED OFF THE FINAL; I TURNED THE BE65 TO A 270 DEG HDG AND CLBED TO 3000 FT BECAUSE OF THE 2700 FT MVA. THE ARR 3 CTLR TURNED THE E145 S FOR RE-SEQUENCE AT 3000 FT NOT NOTICING THAT I HAD TURNED AND CLBED THE BE65. I SAW THE E145 TURNING TOWARD THE BE65 AND I IMMEDIATELY DSNDED THE BE65 IN AN ATTEMPT TO MAINTAIN SEPARATION; BUT SEPARATION WAS LOST. CAUSAL FACTORS: 1) DFW REQUIREMENT FOR MEACHAM S TO HANDLE IFR DEPS OFF GKY ARPT IN ANOTHER SECTOR'S AIRSPACE. 2) THE MEDICAL EMER INBOUND. 3) DEVELOPMENTAL CTLR ON ARR 3. 4) 7110.65 REQUIREMENT TO MAINTAIN 1000 FT VERT SEPARATION OVER PERMANENT OBSTRUCTIONS. CORRECTIVE ACTIONS: 1) CHANGE PROC FOR ARR 3 TO HANDLE IFR DEPS OFF GKY ARPT IN A N FLOW. 2) CHANGE 7110.65 TO REQUIRE ONLY 500 FT VERT SEPARATION OVER PERMANENT OBSTRUCTIONS.