ZDC CTLR B757 THROUGH HOLDING PATTERN OF ANOTHER ACR WITHOUT ENSURING REQUIRED SEPARATION.

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BOTH ACFT HOLDING IN 2 DIFFERENT HOLDING PATTERNS. ACR #2 CLRED TO LGA VIA ALTERNATE RTE -- CCV.SWV.SIE.CAMRN.LGA -- AS INSTRUCTED BY AREA MGR IN CHARGE. THE RTE WAS DUE TO TSTMS ALONG NORMAL RTE. ACR #2 RTE WAS THROUGH THE HOLDING PATTERN OF ACR #1. ACR #1 WAS ISSUED A 350 DEG HDG TO CLR ACR #2. ACR #1 DID NOT ACKNOWLEDGE THE CLRNC AND I DID NOT REALIZE THIS. WHEN I OBSERVED ACR #1 TURNING W IN THE PATTERN; I ISSUED VECTORS TO BOTH ACFT. THE ACFT WERE SLOW TURNING EVEN THOUGH I ASKED FOR EXPEDITIOUS COMPLIANCE. ACR #1 CLBED DUE TO TCASII ALERT. OTHER FACTORS WERE -- NO SUPVR IN AREA; AND NO HELP AVAILABLE DUE TO LATE NIGHT STAFFING. CONTRIBUTING TO THE MISSED READBACK WAS THE FACT I WAS HAVING TROUBLE PUTTING THE RTE IN ON ACR #2 ON THE NEW DSR EQUIP. SUPPLEMENTAL INFO FROM ACN 476926: FOLLOWING HOLDING AT FAK (FLAT ROCK) FOR APPROX 1 HR; RECLRED BY ZDC TO LGA. WE TURNED TO AN APPROX HEADING OF 100 DEGS AND HAD BEEN ON THAT HEADING FOR A SHORT TIME WHEN ATC DIRECTED AN IMMEDIATE R TURN TO A HEADING OF 180 DEGS. AT THE SAME TIME WE RECEIVED AN RA ON TCASII. THE OTHER ACFT STATED THAT THEY HAD RECEIVED A TCASII RA AND HAD CLBED SLIGHTLY.