I adopted a dog from Portugal, another history in itself, but did consider a greyhound.
The Asso I contacted recommended enrolling them in sports for dogs. I imagine there are more greyhound clubs in the UK than here (in a deserted mountain region in France!). Also that they do have diet problems...
I raw feed my dogs, and they thrive on it. I get a variety of meats, tripes etc. Frozen. I cook up frozen veg and mash it. I make 2 days supply at a time.
Maybe a change of diet, with, so I have been told, pumpkin in it. Meant to help with tender tummies.
It's quite a thing finding the best diet and lifestyle for an adopted adult. Especially those who were not well treated before.
Good luck to your DD, I'm sure with time it will sort out.