You are in a very good position and I would be VERy surprised if they let you go. I'm sure they would take what they could. Its how I got my boss to go against the part time rules (min 3 days) and give me two.
Stand firm, they need you. Smile and tell them you are on along waiting list for day care and you will increase your hours if you get a place. They can't argue with that, nor pick on you for wanting to stay home.