I am also interested in swimming for babies in the Nyon area. Just a heads up so that you don't make the same mistake as I did. I took my 5 month old son to the thermal pool in Divonne this afternoon and can report back that it was a huge waste of money (20 EUR entrance fee) and time. The facilities are quite run-down and not at all baby friendly. The only real advantage was that the water is 30C and has some sort of healing qualities. Hmm, I wonder if the little mouse will sleep through the night tonight!!!

Good luck and do let me know if you find somewhere.