Are you anywhere near your NHS pension, Rob? ... if so, it's probably best that you hang in there, Mate.
Otherwise, what makes you imagine things are any better outside (the NHS), if that's what you mean.
For some reason, I find myself feeling sorry for your dog.

Why not try calling your manager's bluff? Let's see if the course is
really that important. After all, even if you get a result with the union (and you may do), you're still not going to be "flavour of the month" with your manager. Sometimes, when dealing with a fox, you have to play the fox.
By the way, in my opinion, 2 hours is too far; if the NHS was properly organised, they should offer accommodation at the hospital nearest to the course venue.And (just out of interest) - and a PM may be in order - is your manager a biomed-type, or (as I have known) someone who has been "parachuted in" from another "trade"?