Next time you are in Taipei, you should try the Wan-Hua sports center’s pool. Their kiddie pool has very shallow to water 90cm deep, and it has two lanes on the side so kids can practice swimming without going into the “big pool”. We stayed in there for forty-five minutes and didn’t feel cold.
As an aside, Nankang sports center has swimming classes especially for autistic children. One is now running on Thursday afternoons. It looked like a fun class, chaotic and lots of smiles and laughter from the instructor and assisting adults. The kids were getting some good exercise, too. I guess you just ask at the front desk or poolside for more information.