PA-44-180 instructor reported a mechanical problem with the nose wheel steering.

Narrative

Flight crew were going to conduct a local dual training flight at ZZZ. After starting engine and proceeding to taxi to runup area; IP (Flight Instructor) noticed the turning radius was wide and overshot the centerline while on the ramp. The IP applied brake and differential thrust to help complete the turn to the left; thinking this was because the SP (student pilot) was not adding in enough rudder as this was the first flight in this type of aircraft for the SP. After runup and receiving taxi clearance from ZZZ Ground to taxi Runway XXR via Taxiway 1; Taxiway 2 the flight crew proceeded to turn left onto Taxiway 1 from the ramp and again the turning radius was too wide; overshooting taxiway centerline; prompting IP intervention to return to centerline. Upon turn left from Taxiway 1 to Taxiway 2; the turn was once again wide; IP looked down and saw the student was completely depressing the left rudder however the turning radius was still too wide to maintain the centerline during the turn. The IP pressed the left brake to assist the aircraft in the turn however this caused the aircraft to sharply turn to the left. After seeing this; the IP released their foot from left brake; after doing this the aircraft suddenly turned to the right; IP heard skidding noises from the tires (IP noted skid marks from the right tire after the occurrence). The IP closed the throttles completely and applied both brakes and stopped the aircraft before approximately 2 feet from the edge of the taxiway. The IP contact ZZZ Ground and informed them they were facing off the taxiway with insufficient space to make a 180 degree turn to make it back onto the taxiway. The aircraft was then towed back to the ramp and squawked for maintenance action.