I'm not sure that I can help you with this!!

It can be very frustrating to be on the end of a computer, nearly have the answers, but....not quite.
The best advice I can give at the moment is to act stupid and see what develops.

Sounds weird, I know, but the bitch is very new to you, her past is mostly unknown and you are very concerned about her.

Can you phone or write to the breeder you got her from? If you can, ask if they bred her. If they did was she kennel or house raised? If not where and when did they get her? (I suspect that she was bought in, not bred, and failed to live up to expectations.)

On the acting stupid - shut the bathroom door. Pretend you haven't noticed she likes it in there. (Everyone in the house has to be trained to shut the bathroom door.) If the dog sits, runs to, scratches at or in any other way tries to draw your attention to the fact that the door is shut you must pretend that you have totally forgotten that you have a bathroom, let alone a dog.

When your brother, or anyone else, comes into the room where the dog is, get them to pretend their stupid too!! - They just don't notice there is a dog there!!! Whatever the dog does, pay attention only to your guest and get your guest to only pay attention to you.

This gives a very new dog the signal that the new leader in it's life is in control and no matter how the dog wishes to react it will be much safer to recognise that you are in control and are able to determine who is safe to let into the house.
If the dog chooses to run away it does not gain support or reaction....even if it then decides to pee outside the bathroom door... as you, as leader, have more important pack members to deal with.

When you are out with dog and let her off lead I would suggest you get a long line. (I loved your description of the dog being "snobby" - that is just the way it looks!) The looking away, snobbily, is an avoidance (as you said) or a dominance signal.

To sum up - I think you have a very unsettled animal that is trying to cope with a great deal of stress with no idea of how to do it.

Be aware that although she is displaying fear and stress she is also showing some dominant behaviour. She is doing her very best to cope and is failing. It is up to you to show her that she has someone to rely on, someone that will protect, direct, love and do what is best for her. What she needs is a strong role model - if you don't react to a situation that she fears and ignore her reaction to it she will learn to trust you and your decisions on what is safe for her.
The very worst thing you can do is be sympathetic in a vocal or physical way. That will only reinforce that what she thinks is scary is scary for you too. She won't see it as you comforting her, but as you seeking comfort because you are worried and scared too.

Close the bathroom door, get a long line and carry on with life as if she wasn't there, unless she is following your lead.

Hope that helps, let me know and good luck.