C172 ON ILS RWY 35 AT AZO IS GIVEN GAR; INSTRUCTED TO ENTER XWIND IN CONFLICT WITH RWY 5 DOWNWIND TFC.

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MY STUDENT WAS FLYING THE ILS RWY 35 INTO AZO. TWR INSTRUCTED US TO GO MISSED APCH AT THE MIDDLE MARKER; CLB TO 2500 FT MSL AND TURN E TO 090 DEG HDG. AT THE MISSED APCH (MIDDLE MARKER) MY STUDENT BEGAN TO CLB OUT. HOWEVER; THERE WAS TFC ON R DOWNWIND FOR RWY 5 (AZO). I TOOK CTL OF THE ACFT WHEN I SAW CONFLICTING TFC ON THE DOWNWIND. I CLBED OVER THE TFC IN THE PATTERN AND BEGAN A TURN TO THE W TO AVOID THE OTHER ACFT. AZO TWR TOLD US THERE WAS A LOSS OF SEPARATION IN THE TFC PATTERN. I THINK IT WOULD BE BETTER IN THE FUTURE TO NOT ALLOW ACFT TO FLY THE ILS RWY 35 AND GO MISSED AT THE MIDDLE MARKER IF THERE IS CONFLICTING TFC IN THE PATTERN FOR RWY 5/23. HOWEVER; IT WOULD MAKE MORE SENSE TO MAKE TFC ON THE ILS RWY 35 GO MISSED BEFORE THE MIDDLE MARKER FOR PRACTICE ILS RWY 35 APCHS INTO AZO. SUPPLEMENTAL INFO FROM ACN 633635: AZO TWR APPROVED MY STUDENT TO ENTER R DOWNWIND FOR RWY 5 AT AZO. WHILE IN THE R DOWNWIND; I NOTICED ANOTHER C172R AT OUR ALT; HEADING TOWARD US. I THEN TOOK CTL OF THE ACFT AND CLBED ABOVE THE CONFLICTING TFC. TWR THEN CLRED US TO LAND RWY 5. I TOLD TWR THAT THERE WAS CONFLICTING TFC AT OUR ALT. TWR THEN COMMUNICATED TO THE OTHER ACFT TO STAY CLR OF OUR ACFT. WE LANDED THE ACFT WITHOUT INCIDENT ON RWY 5. I FEEL THE PROB WAS CAUSED BY THE OTHER PLT IN THE CONFLICTING ACFT BEING INEXPERIENCED (SOLO STUDENT). ALSO; THE TWR AT AZO HAD ONLY 1 PERSON WORKING BOTH TWR/GND. I FEEL THAT AZO SHOULD HAVE MORE THAN 1 PERSON WORKING TWR WHEN SOLO OPS ARE IN EFFECT.