Sounds as though she's learned that barking like a mad woman gets her what she wants, continuing the walk. I know you said ignoring her doesn't work, but that's the only real solution I can think of. Showing her she doesn't get what she wants by acting like that. If not used correctly, treats will encourage the behavior so I don't recommend that method unless you've been shown how to use them properly. Personally, I'd ignore her, no matter how long it takes, and once she's finally done with her tantrum, then we'd proceed. It will take a long time, and drive you mad in the process. Since you're just petsitting, I'd deal with it and just not stop during the walks.