My friend has also had this problem. She started cm'ing, then got a big dog, kept it in a run in the garden, and a big cage in the kitchen, and still parents were very uneasy.
She lost jobs because of it, and now she has given up cm'ing because the dog is stressed and agressive after being cooped up and separated from its family for most of the time. It was supposed to be a family dog.
I cm also, and don't have a dog as we rent, and are not allowed. But if we were to ever own, I would love to get one, as would the dc. I would think very very carefully about the breed/size/age etc of dog, and talk it over with parents first.
If my dc were at a cms with a dog, I would have concerns, but not neccessarily remove them. It would all depend on cm and dog. I have lots of cm friends with dogs, and they have no problems at all.