Air carrier flight crew reported that during push back from the gate; the push crew exceeded the turn limits of the nose gear.

Narrative

Normal preflight. Ramp crew had informed the Captain that they would be doing training on our pushback. Push instructions received from Ramp Tower and Ground Control to push from Gate XX into the 1 alley. Brakes released and pushback initially started normally. As we began the push onto Taxiway 2 it looked like the push crew were taking us a little wider than normal for the turn into 1. The tug crew tightened the turn radius to make sure they avoided going off the north side of Taxiway 2. The engines were not started. At this point they suddenly stopped and called the flight deck to say that they had exceeded the redline for the towbar turn limit. Tug crew called for Maintenance to attend and inspect the situation. Maintenance recommended we return to the gate and take the aircraft out of service. Aircraft pulled back onto the departure stand; pax (Passengers) disembarked and aircraft swap initiated.Cause: Pushback crew was conducting training on our pushback tug. During pushback both pilots noted the slightly unusual turn radius as we being pushed; but since we knew they were conducting training we didn't feel the need to intervene and interrupt the instruction. Many gates at ZZZ have a simple 90 degree turn involved in the push but some like XX have a more complex maneuver that involve a 180 degree turn and then into an alley. Perhaps training inexperienced push teams on the simpler pushes might avoid a similar situation.