She’s young, IMHO under exercised/socialized and she ain’t no Golden Retriever.
Both Pits & terriers in general are independent thinkers – they were both bred to ACT independently of humans. They weren’t bred to work WITH people like herding or working dogs. In addition, terriers especially tend to be very “busy” dogs…you need to engage their minds and their bodies ALOT.
So IME it takes longer to form that bond with these breeds and you need to be a stronger leader. They don’t just become instantly devoted to you like many of the working breeds. You need to earn their obedience and respect.
I really don’t think she is the right dog for your household unless you are willing to devote much more time to her, so I think alot depends on just how much time you ARE willing to give.
If the 2 hrs a day you give her now is the max you can spare, I really do recommend you rehome her. To give you an example, when my JRT was her age, she was getting walked OFF LEASH through a large wooded park near my home about 3-4 hrs per day total. I walked about 2 miles, she ran about 6 miles dashing back and forth after squirrels, etc.
And someone was home with her almost 20 hrs per day. Oh, and we had a fenced yard as well, so she could go out and play with the older dog. She was ALWAYS raring to go!!
So think long and hard exactly how much you want to commit. There isn’t a right or wrong answer – it’s a matter of fit.
However, if you want to try other things, perhaps a pro trainer could help.
Again, do YOU do any sort of exercise that you can incorporate into the pooch’s day? Like running, biking, riding, swimming, etc.?
Where do you live? Suburb, city, country? Apt? Duplex? House?
Generally speaking, high energy dogs need to go with high energy people, so you really need to be honest about this or otherwise everyone is going to be unhappy.
And by all means talk to your vet about drugs…but do you really want a dog that has to be drugged their whole life to be a companion?
This truly isn’t fair to the dog, is it?