There is a genetic factor to poop-eating, but it can be just flat-out habit as well. The technical name is coprophagia. Its easily helped by giving her either a commercial product (like Deter or something similar you can buy at most pet stores), or sometimes by giving her a spoonful of pineapple or pumpkin in her food.
Her coat issues could be related to her poor nutrition. I've seen dogs going from a poor diet to a good one completely blow their coat and grow a new one. Or if you have not ruled out parasites (fleas, ticks), it could be that as well. Or it could be mange. A vet will be able to tell you more. Its impossible to diagnose something like this over the internet, especially without a picture.
Its a shame that you wont keep her just because she needs some work. Its not her fault she isn't perfectly healthy and quoting Shakespeare. She just needs some TLC.
Lindsay & the Gravity Dogs
"Though she be but little, she is fierce." -- Shakespeare