INSTRUCTOR WITH SPI FLYING ENCOUNTERS DETERIORATING WX. ON SVFR HAS CLOSE PROX WITH SECOND ACFT ON APCH.

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THE PROB WAS CONTINUED VFR INTO DETERIORATING (MVFR) CONDITIONS; LACK OF VISIBILITY AND HVY CTLR WORKLOAD. AS INSTRUCTED BY THE TWR WE WERE HOLDING OVER A GND CHKPOINT JUST S OF THE LOC COURSE AND ON THE EDGE OF CLASS D FOR OUR SEQUENCE FOR LNDG. THE CTLR TOLD US TO 'TURN BASE FOR THE LNDG RWY 24 AND FOLLOW TFC ON FINAL; #2 CLRED TO LAND.' WE HAD TFC IN SIGHT AND PROCEEDED INBOUND. #3 ACFT WAS INSTRUCTED TO FOLLOW US BUT RPTED US 'NOT IN SIGHT.' THE CTLR CANCELED OUR LNDG SEQUENCE AND INSTRUCTED US TO MAKE AN IMMEDIATE L TURN BACK TO OUR 'HOLDING AREA.' WE WERE THEN INSTRUCTED TO FOLLOW ACFT #3. I DID NOT SEE ACFT #3 UNTIL WE TURNED BACK TOWARDS THE ARPT TO FOLLOW HIM. MY STUDENT (STUDENT PLT) WAS FLYING AND COMMUNICATING. I TOOK OVER THE COM WHEN IT SEEMED THE CTLR WOULD BE UNABLE (DUE TO WORKLOAD) TO SPEAK SLOWER. THE COMS WERE ALSO VERY 'NON-NORMAL' AT THIS POINT (SPECIAL INSTRUCTIONS; IMMEDIATE TURNS TOWARDS LANDMARKS ONLY KNOWN TO LCLS ETC). THE TWR CTLR REQUESTED (VIA TELEPHONE) THAT I TAKE OVER COMS SOONER IF MY STUDENT WAS HAVING DIFFICULTY WITH IT. I FEEL THAT I TOOK OVER AT THE APPROPRIATE MOMENT; BEFORE WE WERE IN THE CONGESTED AREA. ALSO; THE CTLR HAD NOT GIVEN ANY INDICATION THAT THEY WERE BUSY WITH OTHER DUTIES; THE FREQ WAS NOT YET CONGESTED. I ALSO FEEL THAT MY STUDENT SHOULD NOT HAVE CONTINUED TO THIS ARPT; BUT SHOULD HAVE DIVERTED TO A GOOD VFR ALTERNATE. WE TALKED ABOUT THIS ALSO.