Dogs can and do get TB, usually from infected chickens, but they can, I believe contract the bovine form and several others. I'm afraid that's all the info I can give as I've never seen a case.
There was a warning put out recently that cats could be a source of infection for humans - but, as usual with the British Government no scientific research has been done on the issue and it is just a guess. We are killing thousands of Badgers every year on the same information - although it is now an area of research that has certain areas culling all badgers, some not culling none and some culling only suspect animals in contact with cows.
We live in hope that somebody will learn something this time around.
One of the theories against Badger culling is that it is domestic dogs and cats that are spreading TB to our cattle herds.
Please keep us up to date on progress and our thoughts are with you, this must be terrible for you.