Alright so I guess I'll start from the beginning. First of all my parents and I (age 21) just moved into a new farm out in the middle of nowhere. We were talking about picking out a Labrador Retriever shortly after we moved there for some minor protection, as large dogs help in that category. My sisters husbands brother had this Great Pyrenees which, him and his wife could no longer take care of due to an over crowded house. It was kind of a pushy situation, so we ended up taking her. She grew up with 3 children around her ages say, 4 8 and 11. BUT she also grew up with the brother, and I knew from watching him play with dogs in the past that he played rough. Tackling them, picking and poking their butts, and holes. Apologies. Grabbing their butts. I know for an absolute fact that she was hit by baseball hats. It's simply the way she reacts around them whenever she feels, perhaps, cornered? Worried?

And I do apologize for the long ill properly worded story. But thank you ever so much for your time.. Back to it.

Knowing these possible problems we still wanted her. We just didn't know exactly how she was, skittish at times.. she got used to us touching her butt and her face and she'd jump back when trying to give her a pet on the head. Conquered that. Now as I said, we got her in a hurry. I don't know if anyone would consider this an impulse decision but it was a free dog and she's absolutely wonderful minus a few flaws. She's playful with one of my shih-tzus and with the other she tends to stay away as shes up in the ages and at times will clamp onto her neck or leg.. Evil little Chloe. I did manage to get some research in before we ended up picking her up and bringing her home, and I did know that Pyrenees are guardians of the land, be it flowers or our chickens (which she barks at) besides that. Being an inside dog (which I do know isn't the greatest lifestyle for a Pyr) She NEEDS a job, and that job in mine and my parents eyes, is protecting me. Even if it's with a growl or a few barks. Here's an example, I'm sitting on my living room with my mother on the couch Izzy is laying down on the opposite side of the couch, in her typical location. My father will sit at the table with his back against her, she doesn't really do any growling or barking at this point in time.. but when night falls (as they are nocturnal dogs, I did imagine this happening) instincts kick in. He's highly efficient around the house and at work, so he'll do all he can to keep on the move throughout the day. Once he stands up, walks to the end of the kitchen and has his back turned doing some dishes or even in the refrigerator, she decides well. I can no longer see who it is in the far end of the house. I believe it's time to pipe in and let out a couple of growls then barks. which, when this happens my two little shih-tzus chime in and amplify it. (Learning bad behaviors from other dogs) That's one major problem I have with her, the growling/barking when backs are turned. Even if lights are on.
Another problem I have as I briefed on earlier was the wearing of baseball hats. Now, my father wears a hat all day no matter what, just the way it goes. She doesn't seem to have such a terrible problem with this at times but others she gets all freaky on him until he takes the hat off. Now, I was playing a game with my nephew the other night and his computer started making a strange noise. We listened for a few minutes and he decided to kneel down and listen to it. Which then my Pyr got all growly and vicious sounding (worse than I've heard before) not too bad, but she seems scared or something. Took me a quick second told him to take off his hat and she lightened up. Even so, she was still freakish after this point. His fear kicked in and she CLEARLY took advantage of that. I'm at the point of possibly finding an appropriate home for her (which would be extremely difficult). I have NO CLUE how to kick either of these problems. Especially the growling/barking when backs are turned. Is there something I should do or say to slowly curb it?
Say she barks, get a hold of her collar (of course not pull tug or yank, I'm not one to train with hatred and pain), firmly say No? And anything else?

I'm truly at a loss, I know this may be too much information but I'm currently in recovery going to programs and staying sober. I feel as if this dog has helped me immensely down the path of sobriety. Most people give up on their dogs around the age of 10 months (which I totally forgot to say up until now). I DON'T want to be that person. I love this dog to death she has been my absolute favorite dog I've ever owned.. I'm stuck and need some major guidance. So, once again

1. Baseball hat problem, skittish around them when taking them off near her she cowers a little bit. Perhaps I should wear one for a week or two and help her realize that it's okay? Not a soul will hit you.

2. Growling/Barking when back is turned. This is a major one right here. Besides saying Izzy - NO - .... wait a few seconds. - THATS ENOUGH - I have no idea what else to say. Maybe I'm messing this dog up in a way I Don't understand.

Absolutely ANY tips and tricks would be helpful at this point. I don't want to lose my only friend. I love her to pieces.. Already feel a wave of depression hit me today, slept for 6 hours when I told my parents I believe the best option at this point is to get rid of her. Please help me.. Thank you ever so much.