At 24 months I would say that 3 hours is too long for a nap and is probably causing the playing at night. Having said that, I don't think I would cut it too drastically just yet - maybe try 2.5h for a little bit to see if that makes any difference.
We went through the same thing with dd1 when she was about 29 months - she would take a great lunchtime nap (about 2h15) and then mess about at bedtime, leading to OT EWs from going to sleep too late. We started out by pushing bedtime later and cutting the nap dramatically (to 1h30) and things got much worse - she got into an OT spiral that was really difficult to fix. After a lot of trial and error, we ended up with 1h45 lunchtime nap and a 12.5h day (so bedtime is 15-20 mins later than it was when this all started).
So, somewhere within all this rambling I'm trying to say: I would cut the nap a bit but don't cut too much too fast.