What to do?

[Wonderwiper]

IMO, you give her no reason to tell you she's looking at other options. All you asked her to do was keep you updated. Since she hasn't yet finalized her plans, why does she need to tell you?

As a parent, I would keep looking for the care that best met the needs of my family.

I think that if you had required a deposit she wouldn't have confirmed a spot at all. She would come back to you after she had finished researching her options if she was still interested. She is clearly interested in something else that works for both children. You allow her to verbally confirm a spot until she finds something else. She has nothing to lose by doing so.