ATC FLC MISCOM CLRNC. WITH NUMEROUS HDG CHANGES AND ALT CLRNCS; EITHER THE FLC MISUNDERSTOOD OR THERE WAS A COORD PROB AT TRACON. RESULTED IN LESS THAN LEGAL SEPARATION WITH ANOTHER ACFT.

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WE LEFT SHV WITH AN AS FILED TO YIP. WHEN APCHING ABOUT 150 MI SW OF YIP; WE WERE CLRED TO FWA CRUXXZ ARR TO YIP. WE CHANGED FREQ JUST AFTER FWA AS WE TRACKED OUTBOUND ON THE CRUXXZ ARR. THE NEW CTLR ASKED US WHERE WE WERE GOING AND WE EXPLAINED THAT WE WERE FOLLOWING OUR CLRNC FWA; CRUXXZ TO YIP. HE IMMEDIATELY CHANGED OUR CLRNC TO DIRECT LTD CRUXXZ TO YIP; SO WE COMPLIED. ABOUT 5-10 MI S OF LTD; HE TURNED US TO A HDG OF 90 DEGS AND DSND TO 9000 FT. WE BEGAN OUR DSCNT ON THAT HDG. AS WE WERE APCHING 10000 FT TO SLO; WE WERE TOLD TO TURN L TO A HDG (I DON'T REMEMBER THE EXACT HDG); MAINTAIN 10000 FT; TAKE OVER ON THE APCH AND CONTACT DTW APCH CTL. I CHANGED FREQ TO DTW APCH AND I ASKED THE FO WHO WAS FLYING IF HE WANTED ME TO CHANGE THE VOR FROM LTD TO THE ILS TO RWY 5R AT YIP AND HE SAID YES. AFTER CHANGING THE FREQ HE SAID HE THOUGHT THAT APCH CTLR SAID INTERCEPT THE ARR. I IMMEDIATELY RETUNED HIS RADIO TO LTD. HE STARTED TO TURN BACK TO THE R TO INTERCEPT THE APCH E OF LTD. WE QUICKLY DISCUSSED OUR POS AND I SAID NOT TO TURN ANY FARTHER AND IMMEDIATELY CALLED DTW APCH TO VERIFY THEIR INTENT. HE IMMEDIATELY GAVE US A L TURN TO 360 DEGS AND DSND TO 9000 FT; WHICH WE DID. I ASKED HIM THE REASON AND HE STATED THE TURN AND DSCNT AGAIN AND SAID WE HAD A 3 MI CONFLICT AT 10000 FT WITH ANOTHER ACFT. A FEW MINS LATER HE CALLED US BACK AND ASKED US WHAT WE WERE DOING AT 10000 FT. I EXPLAINED THAT WE HAD BEEN ORIGINALLY CLRED TO 9000 FT BUT WERE STOPPED AT 10000 FT; TURNED TO THE NE HDG; TOLD TO TAKE OVER ON THE APCH AND CALL DTW APCH. THE FLT WAS COMPLETED WITHOUT FURTHER INCIDENT. WE WERE RETURNING PART 91 TO YIP AND HAD BEEN ON DUTY APPROX 16 1/2 HRS. I APPARENTLY MISUNDERSTOOD THE CLRNC AND THE CTLR WHO GAVE IT TO ME DID NOT CATCH THE ERROR.