I am a childcare provider with animals. First off, this should have been an issue that was covered in your initial interview. Most of the time, parents ask this question, if they don't, I answer it for them. I NEVER allow any of my animals to come into contact with my daycare children. On occasion, one would sneak by but I would immediately remove the animal from the daycare and either put them outside, in in a kennel or simply close the door to the daycare. We had (recently put down our Newfoundland and our cat) two dogs and a cat. I asked the vet about having our animals around the children and his answer was very simple. He said that no matter how much an animal is a part of our family, they are STILL an animal and can/do bite at will. Our dog was almost 12 years old, never hurt a flea and still, we kept him away from my daycare children although my own son rolled on the floor with him, pulled on him, all the things children do with dogs. The point being, he was MY son, not a daycare child. As his mother, I get to make that choice. As a childcare provider, I am NOT allowed to make that choice. It is a liability issue.
Another posted suggested that you ask to see your providers insurance policy. If I had a parent who asked to see this, I would immediately look to replace that family. That in and of itself, begs for problems.
I would address this concern with your childcare provider immediately. Express your feelings confidently and kindly. Tell her you are not comfortable with her dog in your child's presence. If she does not agree to do this, I would report the incident to the Licensing Department and change daycares.
I love my animals, I truly do. But when it comes to making a choice between a child and an animal, the child will win EVERY time. It is our responsibility as providers to keep children safe and well-cared for. Your provider has a responsibility to do this. Don't back down.