Did you have a meet and greet with your sitter?
Did you tell her you are expecting her to stay in your home?
Did you tell her how many hours is she to stay in your home?
Did you tell her what hours she is allowed to leave and leave the dog alone?
Did you tell her she can take your dog to her home?
Unless you discussed all this above, you can not "expect" your sitter to do what you want if the sitter hasn't heard all that directly from you. That's why you have a meet and greet.
On the other hand, people have no issues if the sitter tells them she is to leave their home for a few hours, and she asks for a permission to take the dog with them, so the dog is NOT home alone. I've done it. They were happy for me to take the pup home so I can go home and take care of whatever I needed to take care of. The dog was with me. No issues here.
It's hard to say what's "normal".
What is normal is to discuss all needs, wants and expectations before hiring a sitter.