Hi there and thanks for the question.
I think you have hit the nail on the head with what you think is going on. This sounds to be a bit of dominance aggression and maybe also some aggression for other reasons. I think she resents being handled in certain areas (who knows why!) and this is why she snaps out.
Firstly cast your eye over the alpha training bits in the book. If she knows she is the bottom of the pack she is less likely to snap out at her pack leaders.
Secondly obedience is very important so work with her daily on sit, stay and come. The better behaved she is the easier she will be to control.
Now to the few issues you have been having. These are all linked so don't think that she has a million problems that you will never fix.
She sounds grumpy about being touched - and seeing as you can pet her here some times i doubt it is a medical problem.
1) When she comes to see you in the house give her a few pats in the areas where you think she may snap. Only a few pats to start with. If she is good praise her and encourage her, if she responds to treats great!
2) After a few days of managing this give her a few more pats on each occassion but stop short of the number that will annoy her. If she snaps do as you have been doing tell her off and give her time out in a dark room with no toys.
3) Slowly over time build up how much you can pat her in these areas.
Now to the bath and brush issues.
I think if we try and introduce her to these things gradually plus some obedience and alpha training we can get her used to these.
What we want to do is to put these things in a non threatening situation -
1) Brush
Start to leave the brush out in areas she will come across it eg by her bed, toys and food bowl. You can leave a few treats beside it so she is encourged to get close to it and used to its presence and smell. Then start to play some games with it (up to you what
) and encourage relaxed behaviour.
After a few weeks of getting her used to it try to use it again. Do it slowly just like getting a horse used to a saddle.
Start with the smooth plastic side of the brush on areas where she is not sensitive. Use it for a little bit all the while praising her then stop.
Do this over and over again over a few days. Then move to a very soft bristle brush that won't hurt. Again short sessions frequently.
Over a few weeks move back to the original brush, praising and telling off as appropriate (never use the brush to frighten her). And make the sessions longer.
2) The Bath
The same sort of principle is important. Take her into the bathroom while leaving the door open so she doesn't feel trapped. Let her smell and look at the bath and leave a few treats beside it. Praise her when she is good, if she gets to much take her out to her time out (try not to tell her off).
After a few days of this put some treats on the edge of the bath to encourage her to get closer to the bath.
After a few days of this encourage her into the empty bath. Try get her in without lifting but you may have to. If she wants out let her out.
A few more days later get her to sit in the corner of the room and run the water in the bath. Praise her and give her treats. Stop the water and let her go up and sniff it. Then let her out.
A few more sessions later get her closer to the bath with the water running, slowly does it.
The tough bit is making the transition to the bath. Have her standing in the bath a slowly add water from jugs into it (often the taps scare dogs). Make sure it is warm and only fill it up to just over her paws. If she gets snappy tell her off and take her away for 10 minutes then try again.
Slowly build up the water level over a few sessions.
Do the patting training first and then extend it into the bath situation
The bed issue is an alpha issue so working on this will help. Leave a lead on her so you can easily pull her off. Ask nicely first and if she growls tell her off and remove her. Then time out.
If she is too rough to get near ban her from bedrooms by closing the doors until she learns they are a privilege
Good luck with her and please tell me how things go and ask for help as you need it
Todd