I kind of disagree with Lewis's response in the part that, negligence in the Pet Sitter would not change who would be responsible. I feel the Pet Sitter would be responsible.
I don't know if this is right or not but in my opinion the fact that you did disclose to the Pet Sitter that your dog has a history of aggression, it was the responsibility of the Pet Sitter to make sure the two dogs were not in the same area. The fact that the other dog broke out of his cage, I don't feel that it would be your responsibility.
It’s kind of like if two dogs are walking down the street. Dog A is a playful, happy dog. Dog B does not get along with other dogs and is dog aggressive. Let’s say dog A breaks out of his leash and runs up to dog B . Dog B's owners try to pull his/her dog back but unfortunately dog B still gets ahold of dog A, hurting him. Even though dog B is dog aggressive, The owner of Dog A would be responsible. Dog A is the one who broke free and ran up to Dog B. It was the responsibility of dog A's owners to make sure the dog was not able to break free.
Similar to the Sitter. It was the Sitters responsibility to make sure that the dog was not able to get out of the crate. Especially already knowing one of the dogs was dog aggressive. The owner did her due diligence in telling the Sitter her dog was aggressive. It was the responsibility of the Sitter to keep the dogs separated and to make sure the crate was properly locked.
(This is just my opinion but would be interested in how everything turns out.)
Hopefully both dogs are doing well! In the future, I would recommend you find a Sitter who only takes one dog at a time and does not have any pets of their own.
Best of Luck!