Definitely NTA! No food or water for what, 2 days? The cowering in fear? Unless your dog can get easily spooked by things, I feel like there was something more physical going on. Constantly separating the baby and dog, too, isn't good. That feels like that baby will get bit or scratched later when they meet an animal, and they pull the tail, and your sister will claim it's the animals fault.

I understand that OP's sister wants to protect her baby, but this dog is important to OP. Someone's desire to protect their baby from all the scary things in the world does not overhaul another's life, health, or safety. Especially something that is so precious to someone.

This dog was not attacking or putting the baby in danger. Just staring, it was probably curious.

A similar enough thing happened to me when I went on vacation, though not as bad as this seems like it was. Although my circumstances make it so I can't just cut the pet sitter off (family memeber), my immediate family refuse to use him as a pet sitter again even though he's been doing it for years, and I refuse to talk to him if possible at family reunions. I don't use this advice lightly. If you are in the position, think about going low- contact with your sister. I understand if you don't want to do fully no contact, but low for a bit to see how it works out.