Potty training a neglected adult dog

TLDR: Neglected rescue hates being outside or contained and has no interest in conventional training rewards. How can we help her?

We recently adopted a 4 year old beagle/bulldog that was rescued from a puppy mill breeder. She doesn't necessarily show signs of physical abuse, but certainly of neglect. She's very anxious and scared of her surroundings, but most of her issues will just take time and patience.

Our primary concern at this moment that we aren't sure how to address is potty training. I don't think she ever went outside in her previous life as she seems very scared of going outside at all, and she hates having a collar or harness on. We can't pull her outside as she'll lock in those bulldog haunches and there's not much to be done about it. She does, however, allow herself to be picked up. She doesn't like it and just goes limp, but she allows it.

Our current plans have simply been to carry her out and gently walk her around the yard, but if we close the door she panics and after a few minutes starts to pull quite hard to get back inside. If she is unleashed she will run to the door, and if it's closed she starts looking for an exit through the fence. There aren't any, so she then just retreats to a corner and wedges herself in among the fence and shrubs. She is completely uninterested in treats, and shows no positive reaction to praise or affection. She could be out and walked for a half hour with no results, then come inside and immediately pee/poop.

She is slowly getting better being on a leash, but she hasn't done her business outside in a week. I've read through the FAQs and wikis about training that are provided, but with her reluctance to be leashed or even being outside at all has made things extra difficult.

…mostly we just want to know if we are making things worse for her, or if it's something we should just stick with until she gets comfortable. We also saw suggestions of getting vet help with anxiety and such, but we didn't want to resort to that unless it was fully necessary.

Any advice is welcome!