First off, you need to look into your states home daycare licenses and see if you're breaking any laws. You also better up your homeowners insurance and have this women sign an accident release form because if anything happens to her child she can sue you. This is a very serious situation you placed yourself in because there are so many ways you can get fucked over. Research and do everything by the book.
As for requesting she pay you for the entire week, you should have had a contract from the beginning. You can write one up and give it to her now but she might not agree and find alternative care. You are not a daycare provider or nanny so parents are just going to use as a drop off playspace only when they need you. Get your act together and become a licenced home daycare.