PA28 pilot reported rudder trim malfunction caused controllability issues and a diversion to a nearby airport with a suitable runway.

Narrative

This was a check out flight after a rigging service. I flew the airplane previously without incident from ZZZ1 to ZZZ1. The airplane had a freshly overhauled cylinder installed previous to that date. The owner asked me to do the first two hours of the cylinder break in. I did so with him present and without incident. I noted that during the flight the plane would only fly straight and level with rudder trim all the way right and in a skid. With trim neutral the plane would roll slowly but forcefully left. The owner agreed to have the problem checked and Maintenance at ZZZ1 found an out of rig condition with the rudder. The rigging was corrected per the service manual. The owner then asked me to perform a check out flight on the plane for functional check of rudder rigging and ADS-B. Ground roll and run up were normal. On takeoff the airplane immediately rolled quickly to the right; but I was able to compensate using ailerons and rudder. I climbed out to the south and as the plane sped up the noticeable right rolling force dissipated.Above 100 mph the airplane would fly straight and level with the trim and slip/skid indicator centered. I decided to return to land at ZZZ1. On approach as I slowed below 100 mph to landing speed the right rolling motion became much more pronounced and forceful. The wind was also from the left and gusting which made control even more difficult. I had to maintain full left aileron to stay in control below 90 mph. I decided to perform a go-around and on the downwind for ZZZ1 decided it would be safer to attempt to land on a larger runway with more lateral space as well as I could keep the speed up during the flare. I let the ZZZ1 tower know I was having controllability problems; but it was not yet an emergency and wanted a larger runway. I got a squawk code and the tower frequency for ZZZ from the ZZZ1 tower controller. I then made a call to ZZZ and turned into the Class C airspace. I followed the ZZZ tower instructions to land on runway XXR where I was able to make an acceptable safe landing. During taxi I did make a few read back errors on frequency but was fairly shaken up after the incident but the airplane handling on the ground was fine and uneventful. I left the airplane at ZZZ to be checked out by the mechanics before the next flight.