Like you we ran a lot of tests on Khaos to determine why he always had soft to runny poops and why he pooped so much, including numerous fecals, ruled out giardia and even ran the mal absorption test. Once I found out that his mother was hypothyroid we also started testing his thyroids.
He was always very dandruffy. His hives started maybe around the time he was 8-9 months old. At first they seemed manageable, but by the time he was 13 months old they started to really come in force and his hair was falling out. None of the standard treatments worked so my vet referred us to a veterinary dermatologist. By that time Khaos looked like this.
The dermatologist diagnosed him with a severe generalized staph infection secondary to allergies. He seems to have a very weak immune system since he can't fight anything off without antibiotics or it will turn into a large infection in no time. What made this staph infection worse was that Culture and Sensitivity testing showed that it only responded to a few antibiotics. She put him on 800mg of Doxycyclene for about 4 months since the other 2-3 AB listed had severe potential side effects.
When she first suggested the underlying allergy might be a food allergy I was skeptical since I had changed his food from what his breeder recommended (Pro Plan - Chicken based) when his runny poop continued after being in my house for a few months to TotW Sierra Mountain (Lamb based) but it only marginally improved his stool and he continued to poop multiple times a day. The dermatologist however strongly believed that his long history of soft stool and multiple pooping a day are indicators of a food allergy. After the 4 months treatment regiment (including antibiotics, twice a week bath with an Rx Spray and daily spraying with an Rx Spray and a very strict food trial), Khaos looked 100% better.
He is however so sensitive to foods he is allergic to, that even giving him heartworm pills which are flavored or any vitamins contained in gelcaps like fishoil or Vitamin E will break him out into hives or a staph infection on his chin or upper lips. Which is why he is now on Revolution. He also has some environmental allergies and has since been put on medication that is, for the moment, rather expensive. It doesn't completely eradicate his hives but at least he isn't so itchy anymore.
As for his eating everything in sight in my yard, that was and still is tricky. I have 2 other dobes and while it is true some Dobes can be goats, it's nothing like what I experienced with Khaos from the day I brought him home. Actually he was doing it when we stopped at the pet store on the way home to pick up some of the food the breeder recommended and we walked him in the grass, so it isn't something he learned at my house from the other 2. I had several dobe owners as well as a couple of breeders tell me that they haven't seen anything like him and that it is NOT normal. On the advice of one longtime breeder I ended up using an electronic collar since you cannot call him off of it, he is that obsessive about it. I ended up being out there for 3 solid months with him, not taking my eyes off of him for one second any time he was in the yard and using the collar every time he tried to eat grass. I thought I had stopped it completely with that mammoth effort but maybe it was more the fact that Winter set in. He started up again in the spring but not quite as bad, so I went back to using the ecollar. It is better now, but I still have to watch him most of the time or he tries to eat it again obsessively.
He is now on Orijen Six fish. His poop is solid, but he still poops 2-3 times a day and his poop is large. He only gets 3 cups a day so I'm not entirely sure where it is all coming from, since he doesn't have any issues with his weight and clocks in around 80 pounds. I tried cutting his food down some more but then he was loosing weight, so my vet and the dermatologist believe it is the correct amount to feed him with slight adjustments when I see him put on some weight or lose some.
I have been told by his breeder (the owner of the dam) that the sire is very allergic to bees and that his only littermate had a severe allergic reaction to a lepto vaccine (which Khaos didn't receive) after he developed a strange golf ball size bump that seemed attached when he was around 7 months old. However the sire's owner told me later that her dog doesn't have allergies and the dam is the one with allergies. I have no idea who is telling the truth and I am no longer in contact with either of them. But I would be interested to find out if your girl's problems also are at least in part caused by a food allergy.
Either way, I hope you find some answers and solutions. I know how frustrating it can be to try and figure out these kind of issues when all you want is for your dog to be healthy.