My thoughts are it is no way for her to have to live. It cannot be healthy for her to sit by the litter box for 12 hours a day.
You are absolutely right, this is no way for her to live. But she does not have to live this way in your house. By patiently working with her, you have a good chance of turning Pandora's life around for the better. Do you love her enough that you are willing to do this for her? Because if you give her away, there is a big chance that she will just wind up being euthanized at some shelter. But if you are willing, keep reading...
Heidi - aka The Tooter
) is a great cat lady and knows pretty much all there is to know about them, and I agree with her advice, but me, starting off as a dog person, would also spend a lot of time working with those pups to help teach them how to behave around Pandora so that she will eventually see them as friends instead of scary, obnoxious monsters!
You said you've tried to introduce them, how did you do this?
First, we all know how exuberant
puppies can be. When you are ready to start re-introducing Pandora to the pups, make sure you have first spent a LONG time exercising and running those pups around outside, so when they come inside and see a cat, they won't be AS inclined to go crazy trying to play with her.
You should also put the pups inside a crate at first so that Pandora can come out of her "corner" and eventually start to investigate without being overwhelmed. Use her favorite treat (like tuna) to praise her during the times when you are trying to socialize her with humans and dogs alike. This will help reinforce the idea that she has nothing to be afraid or skittish about and will also help to associate the pups with yummy treat time.
Once you have spent a lot of time working on just you and her, and then introducing her to the crated pups, eventually you should close Pandora, Pandora's favorite treat/toys, one puppy and yourself in a neutral room. Keep the puppy on a leash and constantly praise Pandora, and offer her treats especially when she displays any kind of non-skittish behavior around the dog. Also, keep in mind that you want to strongly encourage
her, NOT force her to do anything. If she gets way too freaked out, calmly adjust the situation by backing up a step or two in the socialization process.
Be persistent, consistent and very patient and I'm sure you be able to make a lot of progress with Pandora. Don't give her away