Hmmm..... it’s all over complicated by the lack of a written contract, up here goes.
If the childminder's changed circumstances happened before you gave notice substantially changed the service she had agreed to provide, you can argue that you cancelled because you were not going to get what was agreed. That would mean the usual notice period didn’t apply, and you’d be due a full refund.
The problem in taking this position is that, initially at least, you appear to have indicated your willingness to press on with the arrangement despite the changes. It also relies, to some degree, on you having stated that you were giving notice for this particular reason.
Otherwise, it is fairly clear that you gave her notice because you changed your mind. That wouldn’t necessarily mean losing your whole deposit. The childminder would be entitled to keep some, but not usually the whole amount. Under the Consumer Rights Act 2015, a business can only retain an amount that represents their actual monetary loss, after having taken reasonable steps to mitigate their loss.
But, all those legalities notwithstanding, one also has to consider the childminder has made commitments to return the money. That rather changes the game in your favour, but you will need evidence of that if she later denies it. Ultimately, if you can’t even prove that money changed hands in the first place, then you’re on a very sticky wicket.
Right now you need to be insisting on a full refund in easy instalments. Also see if you can get CAB or a solicitor to assess if you have a case worth taking through the small claims procedure. Some solicitors offer a free short consultation to decide if something is worth the candle, or you may have some legal cover through your home insurance policy.