Very often if the dog has had a rough life they are very insecure and on one paw fearful of screwing up and on the other paw terrified of the change. So they retreat.
How is she on leash? You might simply let her drag a leash or ribbon, so you can get her to go with you to other rooms -- be cheerful and not demanding but "Let's go do ________" or "Let's see what there is to eat!" or "I'm tired --- let's go upstairs and chill!"
Carry treats in your pocket. so you can reward ANYTHING and everything. Shop around and be creative. What might be a "treat' to you might not be one to her. My dogs drop dead favorite is a little cereal called 'Puffins" -- it has corn but no gluten (I've got one who is allergic to wheat) but dang, they're crunchy and a bit sweet!
Banana chips .... Gerber Graduates (yeah, baby snacks) banana/strawberry and apples (freeze dried). Dog treats -- yeah that too. Kibble samples.
A good game:
Have some high value treats in your pocket. Bring her near you and have a treat in each hand (closed) - put your fists on your knees and simply say her name. The **instant** her eyes flick to you in response to her name you open the hand under her nose. Wait til she looks away and repeat with the other hand. Her name on your lips becomes the sweetest sound ever!
Practice from across the room. Say her name and when she looks at you toss her a treat. But in this way responding to you becomes a good thing.
It will take you 6 months to a year to unlock everything ... you'll notice when something really unravels her -- yelling? a particular word? people with hats?
I've seen dogs who literally thought their name was "No!" because it was said to them so often.
I had a dog onces as a foster who would cringe and be terrified at the term "Good girl!" because a former owner had beat her with the repetition "You WILL BE a **good girl**" that accompanied the blows. Obviously -- if you find something that unnerves her you will then know to avoid it.
One time I had a foster who had reportedly been a "circus" dog. (little informal flea market kind of "circus";). super well behaved -- did everything the other dogs did immediately. He was an old guy but .... listen?? NOPE. If I was talking I might just as well save my breath because he did NOTHING on command. Now if one of the other dogs would "sit" so would Curley. But not because *I* said so.
Occasionally we'd see him "do" something amazing like leap and turn a somersault -- and have not even one small clue what triggered it.
After a couple of weeks I began to despair we'd ever figure it out. He wasn't deaf ... in fact his hearing seemed astute but *listen*?? Nope.
and COMPLETELY unmotivated by treats. Wouldn't take one on a bet. Now put the same treats in his dish for "dinner" and they were gone. But would NOT take a treat for any reason. ONLY at "meal time". huh? A-B-normal dog. weird.
Finally one day after a particularly unsuccessful time trying to just get him to "sit" on command, he mimicked something antother dog did quick enough to actually be a "response" to my command to "sit". And I literally laughed and clapped my hands for joy.
VOILA!!!!!!!!!!!!!!!!!!!!!!!! HE WAS THRILLED!!!
Duh Callie -- he's a ***CIRCUS DOG*** -- he responded to .... Applause!!!!!
From then on teaching him was a breeze -- if he did what I asked or responded to my voice I merely CLAPPED for him. That was it!!! He had simply been so trained for the circus (you can't be around kids/people and beg for their food!!). And in a circus everything is done with secret "signals" and his reward was "applause". I had to learn to make my voice another "secret signal". But learning he wanted "applause" was the big kicker.
My point is -- be creative and see what THIS dog likes. What is it afraid of? What produces a wag? What produces a backing off response?
Take nothing for granted. And don't assume that just because this dog hangs back in the corner that he LIKES it. He's likely just avoiding what he perceives might be the dire consequences of screwing up.
But the above suggestions of doing obedience -- that's golden. Because that's how you "teach" him how to please you.