As others have said, highly recommend Baby-Gym in Vich, for sport, gym, danse, etc.
In addition, there's rhythmic dance,
http://www.rythmique-nyon.ch/rparenf.htm
The Ecole music de Nyon has some music/danse for young children, not sure if start at 3 or 4 years old though.
www.emnyon.ch
For music/art workshops, there is parent-child classes at the museum in Nyon through la Bulle d'Air
http://www.labulledair.com
There is Gym-Danse in Prangins, not sure if start at age 3 or 4,
http://www.gymdanse.ch/
SB Sport in Gland also does great sport classes, not sure of the age requirements though,
http://www.sbsport.ch/fr/
At the Signy center there is a private creative kids garderie, English-French, maybe an option for short breaks.
http://www.creativekids.ch