I suggest in the meantime you work with your dog to get her past the aggression/obsession with this other dog.
My dog has leash aggression meaning that he can hang with any dogs most any time but when he’s on a leash (when we’re walking) he loses his shit when we’re within 20’ of another dog. So walking past dogs in their own yards has been a challenge, let alone passing other dogs on the street.
We went to training at the local Humane Society to specifically work on this. I have to load up on treats when we walk and when another dog walks by, we stop and I get him to focus solely on me by telling him “watch me” and giving treats slowly (I have big crunchy treats that I break apart so there’s a lot of fumbling around to watch).
When we walk past a barky dog in their own yard, we cross to the far side of the street (to give a buffer) and I talk to Grady and let him know that it’s ok, he’s a good boy, the other dog is a good boy, and I’m here and It’ll be ok. Once we’re past the offending dog, he gets treats.
It took a LOT of constant work but he’s tons better. He can walk by dogs in yards without incident. Crossing dogs on the street is still a problem for him but he can focus quite well on treats. Used to be that he would start losing his shit just coming up to one yard, even if the dog isn’t there. Now we can walk by that yard and the dog can run up and start barking and he doesn’t even flinch.
So I would suggest trying this on a leash by your fence, both inside the yard and outside. Let her hear the dog barking, get her attention with treats, and have her sit and take the treats while the dog barks away. Lots and lots of praise and reassurance. Let her know that you know that the other dog is there and it’s all good, you have it handled.
I’ve found that in my neighborhood at least, when my dog ignores the other dog, the other dog eventually stops. I’ve trained them all
ETA the way the Humane Society trainer explained it is that the stuff my dog was doing was coming from immediate innate Beast Mode reaction, and by giving the treats you are able to divert the reaction from being Beast Mode to Happy Time Treat Mode.
Oh yeah, also, he walks with a Freedom Harness to help me manage him better when he’s losing his shit. Everything else he has been able to escape out of.