C172 flight instructor reported in flight engine roughness and the need to divert to an alternate.

Narrative

On Day 0 I was on a training flight with my student in Aircraft X. Our planned flight was IFR. We departed on our initial leg of ZZZ to ZZZ1 at approximately XA29 central. We initially climbed to 6000; but had been instructed to descend and maintain 4000 by Approach Controllers in preparation for our arrival into ZZZ1. At approximately XA53 central on Day 0 we experienced a drop in approximately 500RPM and violent engine shaking at 4000 feet approximately 5 miles southwest of ZZZ2. I immediately took controls and began a diversion turn back towards the nearest airport; ZZZ2; and reported the irregularity to the Approach Controller we were on with (ZZZ Approach). At this time I [requested priority handling] given the extreme engine roughness. We got a number from ZZZ Approach to call on the ground when safe. After approximately 1 minute of sustained RPM loss and violent shaking; the engine RPM returned to near normal and the shaking mostly subsided. I maintained 4000 feet until I was within gliding distance of the runway to be safe and chose the runway favoring the winds (Runway XX). Once landing was assured I flew overhead and entered a left downwind for Runway XX and descended accordingly maintaining enough altitude to glide to the runway. At approximately XB00 central we touched down safely at ZZZ2 and taxied to the ramp. I believe a contributing factor in this issue is lack of adequate maintenance by the maintenance team. For over 6 months (if not longer) many flight instructors across the fleet have experienced unexplained engine issues and repeat squawks for the same issues in the same aircraft with little to no explanation from maintenance. Additionally; after the accident that occurred in a school aircraft (Aircraft Y) before; many instructors were silenced about their genuine maintenance concerns by school management who would not allow any discussion or voiced concerns about our maintenance. This is not safe and does not represent a just safety culture.