Advice on scared dog who knows nothing

So my neighbors have this 2 y/o dog that I've been feeding, she's free to roam and i know the owners don't feed her very much and want to get rid of her so if future cat introduction goes well I think I'll take her on (she's good with their cat). Never been indoors, never been in a car, never been to a town or city, used to be tied up so she's probably gonna hate a collar. I'm making good progress with her I think, she used to bark at and/or run away from me but now she willingly sits with and follows me, accepts pets, belly rubs, licks me and eats from my hand. Her mother was either run over or shot for biting, so she's understandably scared of people, I don't know if she's been beaten but I was trying to train her sit today and sometimes she'd do well or sometimes she'd shy away when I raised my hand above her head as if I was going to smack her. I have had to yell around her in the past because when her mother was around, that dog would attack you if you didn't scare her off, and the two of them were always together. and I feel bad if she thinks I'm going to punish her if she doesn't do what I say. Once she refused to un-sit until I put her treat on the ground because I guess she was scared of not following the rule I was teaching her? I stopped training as soon as she looked scared. Not sure how to better start it up again. She's really starting to trust me but still gets scared of fast movements, or sometimes just walking up to her. I've just been sitting out with her for hours and petting her recently so that's helped a lot but I need to figure out how to car train and muzzle train her so I can take her to the vet for vaccines and neutering (cannot afford her having puppies. Really hope i can get her fixed before spring). Doing plenty of research but wanted to see if there was anyone here who had a similar dog and/or had some advice. Sorry if this is too unspecific or the wrong sub.

Tldr: trying to earn trust of and train neighbor's potentially abused dog who I had to yell at in the past so I didn't get mauled by her mom. Mostly looking for where should I start apart from sitting with, petting and feeding her and what mistakes should I avoid or training material to check out.