Lovemygirls, do you you need the money right now or do you just want to ensure you get it in the end? This woman is out of work and has no money, so it's really going to be difficult (impossible actually) for her to pay you. You are right of course. She owes it to you. But, at the end of the day, it is not possible for her to give you something she doesn't have.
So, what if you cut her a bit of slack but still demanding full payment in the end. What I'm thinking is ask her for half the fees for eight weeks running instead of full fees for 4 weeks running. That way you have made an effort to be flexible, but you are still asking for full payment. And, if it does end up in court, you can demonstrate that you did make an effort to be flexible.
I do see your point that she signed the contract and she owes it to you. But I just don't think she sounds like she will be able to do it. So, you might need to consider what sacrifice you are willing to settle for. If you go in hard and say no no no. I want it all and you don't budge on anything, she might just take a hike and you won't get anything.
How much money are we talking about? Will you really be better off if you have to go to court, take time off of childminding which will in turn effect other families, and so on.
Also, in the meantime, you say no one will want to pay your holiday cover. That's probably true, but if you need more money you could surely offer a babysitting service at this very busy time of year. We dropped the kids off at our old childminder a few weeks agao while we did some Christmas shopping. This was great because of course you can't buy gifts that are supposed to be from Santa while the kids are with you.