C.S.
Have you checked Home Sweet Home? They are in Culver City. I don't know if they have openings but they are year around and very flexible with schedule and hours. They definitely potty train. Both of my girls went there and I truly can't say enough good things. Also you could look at Temple Akiba nursery school in Culver City. I have heard wonderful things and personally know the director. You do not need to be Jewish to attend. Good Luck.
C