Tiny savage dog

[Pleasedontputthatthere]

We have a two year old Border Terrier who was initially lovely to all dogs and people. She is now lovely to all people (unless they are wearing hats) and some dogs. Noticeably, she is particularly shouty/aggressive to really big dogs (ones that could eat her as a snack) and puppies. I have tried distracting her with treats/look at me when a trigger dog is passing but this doesn't work. She escaped the gate yesterday (son left it open) and a sausage dog barked at her and she pinned it against the fence, I shouted her name loudly and she stopped and immediately came back.

I wonder if it would be better to try and do a sharp pull back and a 'no' when she starts lunging/trying to eat puppies, rather than distracting her.

Any ideas please?

Do you start the distraction in time or when your dog starts reacting? I've read they can build up layer upon layer of stress so react more and more so you need to try and react before they do. Easier said than done, I know.
My dog was fearful of big dogs like Alsatian's and would bark at them when we walked past. If she was off the lead and we'd encounter one, she'd stop and then run in the opposite direction. I started getting her to focus on me rewarding her with treats when she was looking at me and not the other dog as we walked past. She is now not fussed by them and just minds her own business.

Yes, that's worth a try. Alsatians are her nemesis too!