I don't think she sees Carter as a threat. She doesn't seem to act like that in any way. If I'm brushing him, she'll come up wagging, then when she is close enough, she figures she can get in his face about not submitting. Basically, I have to lock her up if I need to brush him. I have not been impressed with having her growl with my face inches away. About 1/3 of her attacks are when I am out there. Unfortunately the other 2/3 are when they are out there alone which is a lot more of the time. That is one big part of the problem. These are working LGDs. They are supposed to be working independently. Everything I've been reading and what I see people here saying is basically, don't let them be together unless you are there controlling the interaction. That just is not possible for this situation and it seems like the more I correct her behavior, the more she is determined to make Carter pay for it afterwards. It just seems like blatant jealousy for lack of a better way of describing it.
I confess to being more than a little annoyed with the prior owners. I very specifically asked if she was dog aggressive and they led me to believe that she was not. They said she was dominant to their female lab but played with her too (sent pics of that) and that she got along well with their male Pyr. They did NOT tell me that they had another younger female Pyr, that the Lab had puppies, etc. I didn't find out those things until after she was here already. The more I find out, the more holes there are in the story I got from them.
This is what scares me about rescue. Now you love her, and you are in a painful situation. I wish people would be more honest when rehoming a pet. I'm sure most people are, but that is just an AWFUL thing to do to a nice, loving person who is trying to do a good thing. It isn't good for the dog either.
I hope you can work something out.
I'm so sorry....