PLT VECTORED INTO FLT PATH OF A DEPARTING ACFT RESULTED IN A NMAC.

Narrative

AFTER TAKING OFF IN ROCKWALL; AN ARPT ON THE E SIDE OF DALLAS; TX; WE CLBED TO 3500 FT MSL AND CONTACTED REGIONAL APCH ON 125.2. WE HAD PLANNED TO CIRCLE DOWNTOWN DALLAS AND AFTERWARDS FLY OVER DFW ARPT BACK TO FORT WORTH. AFTER WE MADE THE REQUEST WITH REGIONAL APCH TO CIRCLE DOWNTOWN; WE WERE HANDED OVER TO DALLAS LOVE APCH; WHO TOLD US TO FLY DIRECT TO DOWNTOWN DALLAS AND DSND DOWN TO 2000 FT MSL. WE PASSED DOWNTOWN DALLAS ON THE N SIDE AND STARTED A TURN TO THE L TO START THE ORBIT. ON A HDG OF APPROX 150 DEGS WE WERE ASKED BY LOVE APCH TO MAKE A R TURN TO HDG 360 DEGS BECAUSE A B737 WAS TAKING OFF TOWARDS THE S OUT OF DALLAS LOVE. WE COMPLIED WITH THE INSTRUCTIONS AND PROMPTLY STARTED A STANDARD RATE TURN TO THE R. WHILE I WAS TURNING THE AIRPLANE; WE SPOTTED DALLAS LOVE FIELD AND WONDERED WHY WE WOULD HAVE TO TURN TOWARDS THE ARPT TO AVOID TFC. BUT BEFORE I COULD ASK APCH; THEY CAME BACK TO ME TO TELL ME THAT I HAD TO TURN R TO 360 DEG HDG. I INFORMED THEM THAT WE WERE ALREADY ESTABLISHED IN A R TURN AND THAT WE EXPERIENCED A STRONG DRIFT DUE TO STRONG WINDS (190 DEGS AT 33 KTS). WE SPOTTED THE B737 ON OUR 2-3 O'CLOCK POS. NOW THE CTLR WAS INFORMING (SCREAMING) US TO TURN R; WHICH WOULD HAVE MADE US TURN DIRECTLY INTO THE B737; LABORED THE R TURN AND TURNED SHARP TO THE L TO AVOID THE TFC. I DO NOT KNOW WHY WE WERE REQUESTED TO TURN R IN THE FIRST PLACE; SINCE WE WERE EXPECTED TO STAY E ANYWAY. THAT I FOUND OUT LATER. A TURN TO THE L WHICH WOULD HAVE BEEN SHORTER DISTANCE WOULD NOT HAVE CAUSED THIS PROB IN MY OPINION; OR A TURN AWAY FROM THE ARPT INSTEAD OF TOWARDS IT.