I'm glad this thread hasn't been all bashing (like some other threads like this one... :/ ) and it's awesome that you are improving her life. In all honesty, I would've done the same as your nieghbors, they really aren't "stupid". I also don't understand why Roxy can only sleep in the back porch sometimes...

Get her on HW medication ASAP! I know plenty of people whose outside dogs struggled and died from HW's. She absolutely needs to see a Vet, but, I wanted to add that my sister has a Lab that is outdoors all the time except for at night, and he is also quite thin even with really good food (Diamond and raw). You cannot see his ribs, but they're very palpable. Outdoor dogs need many many times the calories of indoor dogs to regulate their body temperature. Like, 2x more food or more! Their bodies have to fight freezing temperatures, which burns loads of calories. This is another reason you can tell your Mom - it's very hard on her body, and requires much more food therefore much more cost, for her to live outside.