MLG VECTORED DURING CLIMB TO MISS TRAFFIC AND THEN HANDED OFF TO NEXT SECTOR ON CONFLICT HEADING WITH COMPANY ACFT. CTLR INTERVENED; BUT NOT BEFORE SEPARATION LOST.

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DEPARTING FROM BWI ON CLBOUT TALKING TO WASHINGTON CENTER. CLRED TO FL230 AND ABOUT TO MAKE TURN TO INTERCEPT 235 DEG R INBND TO WOODSTOWN VOR. ABOUT THAT TIME GOT CALL FROM CENTER TO TURN RIGHT TO 090 DEGS AND EXPEDITE THROUGH 17000'. (I WAS WORKING RADIOS; CAPT WAS FLYING.) OUT OF 17000' I CALLED CENTER AND ADVISED OUT OF 17000'. HE ACKNOWLEDGED. OUT OF 18200' HE CALLED AND SAID; 'LEVEL AT 18000'.' I SAID; 'ROGER; GOING BACK DOWN TO 18000'.' HE THEN SAID; 'TURN LEFT TO 030 DEGS.' HE ALSO TOLD US THAT WE OVERSHOT THE RADIAL WHICH OUR RADIOS DID NOT CONFIRM. AFTER SWITCHING TO NEXT CTLR; WE WERE TOLD THAT THE PREVIOUS CTLR HAD A POSSIBLE TFC CONFLICT WITH AN ACFT AT 16000' AND OUR AIRPLANE. THEREFORE; THE TURN TO 090 DEGS AND THE 'EXPEDITE THROUGH 17000';' BUT THE TURN PUT US IN CONFLICT WITH A COMPANY MLG Y AT 19000' IN THE NEXT CTLR'S AIRSPACE. THEREFORE; THE 'LEVEL AT 18000'' REQUEST. THE NEW CTLR SAID IT WAS NO FAULT OF OURS. THE ONLY DISTURBING THING WAS THE JERKY HANDLING OF OUR ACFT AND THE WAY HE SEEMED TO WANT TO BLAME US.