Your test on the caliper pistons was appropriate. You were able to push them in and they came back out when applied.
You should also do as someone else suggested above by jacking up the car and seeing how the two front wheels spin to see if one the calipers is hanging up.
What is strange is the pulls right under normal driving and then left when you apply the brakes. The only thing that I can think of that could cause this is a restricted brake hose or brake line so that the right brake doesn't fully release and then doesn't properly apply when you brake. Look for a kinked or rusted line or a deteriated brake hose, probably on the right front.
