Thanks for answering my questions. I really appreciate the additional information.
Obviously it's hard to know for sure what's going on, however, if it looks more like the first clip, then it could very well be that she's got something called tracheal collapse...which is actually pretty common in dogs. I have a maltese cross who has it and has an attack a couple times a week for years with no problems.
This can be a chronic, degenerative issue that could impact the health of the dog. You can find more information on this particular issue here( and although this is an article about small breeds, there are large breeds with this issue as well): http://www.toybreeds.com/health.htm
The other thing I was thinking was the possibility of this being some kind of cardiac cough since we don't really know anything about her history. Dogs get congestive heart failure (also known as CHF) just like humans. This is when the heart doesn't pump as effectively as it should, which causes fluid to build up in the lungs, making the dog cough. Since you said it looks like the first video, I feel pretty confident that it's not CHF, but it bears mentioning anyway...just to be safe.
Tracheal collapse is normally treated with a cough suppressant and steroids, and although I understand there are no vets in your area, it's not a bad idea to find one somewhere nearby.
There's another good site that goes over treatment options here:
I hope this helps!!