C550 FLC MISHANDLED BY APCH TWR CTLRS AT ACY.

Narrative

I WAS CLRED FOR VOR 31 APCH IN MARGINAL VISIBILITY CONDITIONS (3 MI) WHEN I WAS ADVISED A CITATION II WOULD NOW BE AHEAD OF ME ON A SHORT APCH. I WAS NOT GIVEN A HDOF TO TWR. WE PASSED THE FAF AND HAD THE ARPT IN SIGHT. WE DSNDED VISUALLY FROM THAT POINT. THE CTLR WAS BUSY WITH OTHER TFC AND WE WERE NEVER HANDED OFF; NOR WERE WE ADVISED OF THE LOCATION OF OUR TFC AHEAD. WE WERE APPROX ON 2 MI FINAL WHEN THE OTHER CITATION; WHO I THOUGHT WOULD HAVE BEEN ON THE GND A LONG TIME AGO; WAS TURNING FINAL RIGHT IN FRONT OF US (APPROX 1 MI). I REALIZED THAT WE WERE NOT ON TWR; SO I SWITCHED OVER FROM THE BUSY APCH CTLR TO TWR WHO WAS ALSO ON THE RADIO. WE WERE SLOWING TRYING TO PROVIDE SPACING BUT STILL CONTINUING. THE CITATION AHEAD STOPPED ON THE RWY AND WAS ADVISED BY TWR TO MAKE A 180 DEG TURN AND TAXI BACK; WHICH BASICALLY STOPPED ANY ATTEMPTS OF CLRING THE RWY FOR US TO LAND. I CALLED THE TWR AND ASKED WHAT HE WANTED ME TO DO. I ALREADY HAD INITIATED A GAR. HE SAID 'GO AROUND' AND 'CONTACT APCH' WHICH WE DID. WHEN WE CALLED APCH; HE TOLD US TO CONTACT TWR; AS IF HE JUST REALIZED THAT WE NEVER WERE HANDED OFF. I SAID AGAIN 'WE ARE GOING AROUND.' HE SAID AGAIN 'CONTACT TWR' SO WE DID. TWR SAID 'CONTACT APCH;' SO I SAID 'JUST CANCEL MY IFR AND GIVE VFR TFC BACK AROUND.' HE SAID 'OK' AND WE LANDED. I'M NOT SURE WHO'S AT FAULT; BUT THIS SURE WAS UNORGANIZED.