I agree with Bluenoselover, praise your puppy big time every time she goes outside. Try taking her to the exact spot shes peed on before. I used to take our puppy outside in my robe and slippers in the winter and wait and wait. The dog would get cold and tired of waiting, so she would sit on my furry slippers to keep warm. We must have looked pretty stupid, and when we came in she'd do the same as yours, pee on the floor. Once she got the hang of housetraining though, she never had an accident again. Our other dog does the Bull Thing occasionally, we just ignore it.
I call it the pealing out method, they do that to mark their territory (when going out side). Now it sounds like you got a little fiesty puppy on your hands. But the best thing you can do for your pup is ignore it, don't say anything when he/she does that and don't acknowledge it. Walk away. Then come back and ask her to sit and when she does give her a treat and "throw a party." This will let her know that her current behaivor is not to be accepted and if she listens to you she will be rewarded. With puppies it is hard, i know, but the thing you gotta remember is Calm and assertive Just like the dog whisper says..lol. As far as potty training goes, thats the worst part of having a pup.. Hands down. Just be patient run around with her play with her out side, and when she goes be quite and then right after give her a treat and throw another celebration. It's all about rewarding good behaivor and being able to ignore the bad. Just like when she starts chewing on things dont acknowledge it, just grab a bone and give it to her so she knows what to chew on and tell her that she is a good dog for chewing on the right thing. Even with your frustration with potty training reserve yourself and just put her on her leash, ask her to sit before leaving the house and make sure your the first one to go out side and not the puppy, and then again reward her when she is doing good.