SH,
I have a similar issue with my SIL. It is not about pets, but she does everything possible to distance my sister from me, and it has worked. But its worse than that. My sister becomes a totally different person when she is around. Withdrawn, uncommunicative, unable to take decisions. So hard to watch.
And the problem is, she really has won in a way becuase family is important to me and I do not feel that close to my sister, and I don't really like her that much when the GF is around.
I hate to even type that because she is all I have left as my parents are gone, my youngest sister was killed 25 years ago, and I have a very difficult relationship with my remaining sibling.
But, this is really in the cant control department. Anything I do, gives the GF more power and makes my sister a better target for her. Plus my sister does not respond to my attempts anyway.
So I am trying to let it go for now and be there if the Sh$t ever hits the fan as it usually does with narcassist sociopaths.
But, I HATE to let her win, because that means my sister losing, but there is nothing else I can do - we are all grown women and can make our choices.
As you say, they really do make a kind of spell these people and put others under their thumb. I know as my Ex did it to me and when I see him now I cannot fathom how that happened -- not at all. But at the time, no one could tell me otherwise.
So I feel your pain, but not sure there is anything you can do to save your sister from herself and in my case even trying made it worse because she became more interesting to my SIL.
So, that is a lot to pull out of your posts, and it may be totally different in your case, but I am here if you want to "talk."
Love your pup.