These are three worthwhile northern stops, but not a neat triangle. Pai lies west of Chiang Mai on the mountain road; Chiang Rai lies to the northeast.
The clearest public-transport sequence is Chiang Mai–Pai–Chiang Mai–Chiang Rai. Trying to cut directly from Pai to Chiang Rai creates a long cross-region road day and fewer recovery options if a vehicle or weather problem intervenes.
TAT identifies Highway 1095 as the mountain route to Pai. Treat each Pai leg as real travel time and keep the day after arrival light if winding roads affect you.
For a short trip, choose Pai for a small mountain town or Chiang Rai for temples, art and a broader provincial base. Keep both only when you can give each at least two nights after transfers.
Northern PM2.5 can affect all three, while mountain rain can slow Pai’s road. Current conditions should decide whether the route remains sensible.