Ceviche,
All the posters are right. Get rid of her. She is taking advantage of you. And yes, here being paid well only makes the maids think you are a loaded dumb ass who can throw money away. And they all think expats are loaded and it is their right to get money from you since you have it.
I have had horror stories too, thankfully all the stories only involved money and clothes, and none of them the kids. One almost sued me, I was able to negotiate with her and she sent me a telegram quitting. Now I have one on the books and she will work for me for no longer than 3 months, no dependency and not contractual obligation then. If they are part time I employ them less than 6 hours a week so they can't claim they depend on my income to live.
You need to read the laws for domestic service and know what to expect if you need more help than 6 hrs a week. http://www.trabajo.gov.ar/domestico/derechos.asp
Also, if you think she'd sue you you might have to negotiate. Her ability to sue depends on how many hours a week she worked and how long has she been working for you. Read the law. Her sudden demands on money might be to precisely set you up to ask you for compensation...
Regarding what to tell her. Just say, nicely, that you no longer can afford her services and that she needs to find another place. You will gladly recommend her to some of your friends and thank her for all her help. Don't argue, or explain your reasons or give them anything they can hold against you. It is like breaking up nicely with someone, it is not them, it is you.
Good luck
Pato