Obsessions and high prey drive - new rescue 6 months old GSD
I need help with my new rescue GSD. I have had more than 5 rescue GSDs in my life time, 2 of them were WGSD. My last WGSD just died in January this year, she was almost 14 yrs. I have been looking to adopt another GSD and finally got one from city shelter last week. She is about 5-6 months old, GSD mix. When picking her up last Sunday, she was very gentle and quiet. I was very happy that she is not hyper like the dogs I had. As days progressing, she becomes more hyper, demanding, barking and high prey drive. I walk her 2 short walk and 1 long walk daily and let her run in the backyard. She tries to kill the birds, squirrels and feral cats. I have cats myself, I have to separate her from them. All my dogs are cat friendly. While she was in the shelter, she has kennel cough and on mediation. She has not been spayed due to kennel cough. I will have her spay as soon as my vet check her up.
These behaviors worry me. She doesn't like movements, shadows, chasing and biting her tail. If I'm in her room, she goes nuts because of my and her shadows on the floor, she digs and tries to bite the shadows on the floor. On the first day walking on busy street, she tried to run after passing cars, after a few yanks and 2 days later, she hasn't chased much. She barked at a man who walked very fast passing us. I just notice about fast movements. The first 3 days, she was on the main floor with my sisters. Because my sisters are walking and shadow movements, she was non stopped barking and biting the computer chair wheels. I moved her to a small room on ground floor next to my room.
I have had her for almost a week. I don't know her background because in her record stated that she was found.
This is her daily routine.
5 AM wake up to go backyard to release herself, breakfast then go for a walk for 15 minutes. I leave for work at 7AM, she is in a room by herself.
10AM my sister takes her to backyard, running around for 30 minutes.
3-4PM dinner and go to backyard again.
5PM I come home take her for a 30 mins walk.
9PM go to backyard and last short walk.
She sleeps with light off which she likes- no shadows!
There are 2 types of doors between her room and my room. One is french door which she can see my room and my cats, another is a solid door. She constantly barks at my cats and I have to shut the solid door which is most of the time.
I train her to sit, down, give paw in the evening. She doesn't know NO command yet. She is a smart dog, fast learner and would be good for police dog or sniffing dog. She knows how to get home on her 3rd day. She has blue spot in the back of her tongue, mix with chow chow?. So far, I don't think she is dog aggressive; because I don't let her see my other dogs due to her kennel cough. I plan to take her to training school after she is spayed. I never had experience with this type of high prey dog, I'm afraid that one day she may kill my cat or any animal in the yard.
Is there a way to correct or control her behaviors I listed above? Or I should return her to shelter. I have unsuccessfully put her in submissive position, Cesar Milan technique, she would not stay down.
Thank you in advance for any help.