I don't think there is any way to keep her from seeing the dog without sounding controlling. You said the two of you purchased the dog together, so the dog is at least partly hers too.
She is allowed to separate from you without losing access to her pet.
Granted, the dog might have been reluctant to go to her when she came to visit, but that doesn't mean that will be his permanent attitude toward her.
It seems like your wife is looking to rebuild some relationships that she damaged by the way she left. If you try to block her from doing that, you don't come off as the good guy.
Me: 44 H: 44 Kids: 20, 16, 16, and 10 Together/Married: 22 years H announced he was emotionally detached and considering D: 4/4/16 H announced he is going to try to stay and reconnect: 5/1/16