I think you did luck out, mostly the staff will not let you bring in your dog, they are fussy about even kids, the two legged kind, most ICU's won't even let in a service dog except on a case by case basis. If I were you I'd be prepared to have to leave her or find a "sitter".
So sorry about your Mom hope your Mom can do rehab close to you, that way you can bring your Dad and your dog, your dog will help in her rehab and general cheering up, not to mention you Dad when he is having a good day. This is a lot for you to handle, prayers for patience and lots of love to you.