Did you ever socialize this dog? I don't see anywhere in your post where you have done that... That could be some of your problems.
I have to say...I rescued Maggie, my Shiz mix almost 3 years ago. She is my most difficult dog. Not my Fila and not my Rottie. I would never consider rolling her intentionally as she would bite. But she is used to getting her tummy rubbed when she is on her back, and is fine...I have never believed in the alpha roll, I think it is unnecessary.
I really am not sure what she is mixed with, but we had our work cut out for us when I picked her up from the store that someone dumped her at. She seemed like a perfect angel when I brought her home...as the days wore on and she felt at home, the demon side appeared...
NILIF did not work with Maggie, she didn't care...she would walk off, she would starve before sitting to eat, get a treat or whatever...She has been hard to reach, emotional wise, what I did find out that works with her is... no Ma mm, she does respond to that.
She does love the grand baby though.
We have worked thru most of the issues, but it still takes me and Keith together to trim her nails, she still tears every toy up she can, the big dogs toys...not hers, and she isn't crazy about company...very few people are allowed to pet her...she prefers to stay by herself... and her latest issue, believe it or not, is bullying Brutus over his food bowl. He lets her have it, and walks away...