ACR ACFT DEVIATING FOR WX AND POOR COORD CREATED A LESS THAN STANDARD SEPARATION INCIDENT. ACFT UNDER SEPARATE ATC JURISDICTION.

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LGT Y WAS 30 MI W OF ROUTE SHOWN FLT PLAN. CLE CENTER DID NOT ENSURE COMPLIANCE WITH CTL INSTRUCTIONS (HDG OF 190 DEGS ISSUED). LGT Y WAS DEVIATING AROUND WX W/O MY KNOWLEDGE OR APPROVAL. LGT X WAS WBOUND AT FL310 ON J149; 10 MI E OF EKN. LGT Y WAS SBND 30 MI WNW EKN AT FL310. CLE CENTER BEL-AIR HI SECTOR COORDINATED WITH ME FOR LGT Y TO FLY HDG 150 DEGS TO GO BEHIND TFC. I SAID UNABLE TO APPROVE DUE TO MY HAVING 3 ACFT WBOUND AT FL310. I TOLD HIM TO ISSUE 190 DEG HDG TO LGT Y AND I WOULD ISSUE 20 DEG RIGHT FOR LGT X. THEY SAID OK; LGT Y TURNED EBND INTO MY TFC RESULTING IN 2.3 MI LAT SEP. LGT Y DID NOT CHK ON THE FREQ AND WHEN I OBSERVED THE ALT READOUT GO TO FL312; FL314; FL370; I THOUGHT BEL-AIR HI WAS CLBING THE LGT Y. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: RPTR SPECIFIED TYPE ACFT INVOLVED AS LGTS. TFC VOL WAS LIGHT AND RPTR WAS WORKING A COMBINED POS. TFC ADVISORY WAS GIVEN TO LGT X AND HE RPTED HAVING THE LGT Y IN SIGHT. RPTR TRIED TO GET LGT X TO TURN FOR MORE SEP; BUT LGT X REFUSED TO TURN DUE TO WX. LGT Y WAS DEVIATING AROUND WX ALSO; BUT HIS DEVIATION WAS NOT COORDINATED BY ZOB CTLR NOR HAD THE ACFT BEEN GIVEN A FREQ CHANGE. INTERFAC COORD WAS HAMPERED BY ZOB HDOF CTLR HAVING TO RELAY INFO TO RADAR CTLR. ACFT WERE SUPPOSED TO BE ON XING COURSES; BUT DUE TO WX DEVIATION; THEY WERE ACTUALLY OPP DIRECTION AT SAME ALT.