Hi,
Reading your post was like having de-ja-vu for me. My fella's parents had a black lab that they treated by the sounds of it exactly the same was as your girlfriends parents are treating jade. Constant human food, no walks etc. Their lab ended up at 60kg when he should have been about 27kg according to their vet

, their excuse was always "look at his paws, he's a big lab anyway". It go to the point where the dog could no longer go upstairs, and a 5 minute walk had him out of action for about 3 weeks after.
I know its hard when you have no control over the situation, but I'm very straight talking and even though I say it how it is my mother-in-law actually loves the bones of me

. I constantly had a go and eventually they took him to the vets who told them off good and proper for the state he was in, but no he wasn't taken off them. Me and my other half when we went round (we had long moved out by this point) used to take him out for a walk which shamed them into doing more themselves.
Unfortunatly their dog died from cancer, so actually unrelated to his massive weight problem or all the crap he was eating (including chocolate

). When we were getting our second pup and their was still some of the litter available they talked about maybe getting on too. I told them in no uncertain terms would I let them have one, and that I would tell the breeder not to even entertain the idea of them if they even thought of approaching her. They now do not have a dog, and to be honest I think that is the kindest thing to the dog world.
We take our 2 round occassionally and I have now stopped taking them cuz they insist of feeding them crap even though me and my fella have had numerous arguments with them about it, you don't even want to know how much it kicked off when they fed my boy some quality street a couple of months ago
My only advise to you and your girlfriend is, if she can get her to the vets she works at that would be great, even if she did it behind her dads back? And when you are both there why don't you start taking Jade out for little walks yourself?
Unfortunately some people are so blind, but if you 2 can do a little for Jade maybe it will shame them into getting off their own arses and looking after her properly.
Good luck, I know how hard and frustrating this sort of situation is