A TRACON Controller reported a departing aircraft reported smoke in the cockpit and returned to the airport.

Narrative

Aircraft X departed Runway XXL at ZZZ and shortly after; [requested priority] with the Tower; due to smoke in the cockpit. This was coordinated with my Front Line Manager and I was told ZZZ Tower would keep the aircraft in the pattern for Runway XXC; the pilot having refused a frequency change. I had two impending arrivals for [Runway] XYC and; at the direction of my Front Line Manager; I broke out both arrivals to allow the Tower to return Aircraft X. Aircraft X continued left downwind at altitudes varying between 3300 ft. and 4000 ft. until finally turning base at 20 mile final. This resulted in a second breakout for both Aircraft Y and Aircraft Z behind them. All aircraft landed without further incident; as I am currently aware. The coordination with the tower; pertaining to intentions and instructions regarding the emergency could have been clearer and more concise. The control instructions to and the sequencing of my arrivals; albeit to a different runway; were difficult to make with an unknown variable aircraft; operating under unknown flight rules by the tower.