@SJCJ Thanks for reaching out!
What a cool idea to help your dad and son spend time outside together! While REI doesn't carry any tricycles, we have had customers bring them into our shop so we do have some familiarity with them. In terms of stability, the smaller the wheels the better. Many tricycles come with 26" or 24" wheels, however, a bike like the Raleigh Tristar 3-Speed Tricycle might worth looking at for your dad. It has a 24" wheel in the front, and two 20" wheels in the back, which will help lower the center of gravity of the bike and make it more stable. It also has an internal geared hub which makes upkeep easy. Unfortunately, it does not look like it is currently available to order directly from Raleigh, however, you may be able to find one through your local Diamondack/Raleigh dealer.
Hope this helps, best of luck!