there is no way I'd be doing that car journey with my 11 year old son if he was that unwell.
What do you mean by "that unwell"? No-one but OP knows how unwell he is.
People aren't impressed because they wouldn't sit in a car in their own excrement for hours, so I think they find it pretty disgusting and distasteful that someone would subject their 11 year old to it.
OP has made it very clear that she has no intention of making her son sit in his own excrement for hours. They are stopping once an hour when he can go to the loo, and they are taking plenty of wipes, spare clothes etc so that if he has an accident between stops then, if they can get off the road, they can deal with it there and then. The reality is that he probably won't have an accident and, if he does, the delay before it can be dealt with won't be more than 20 minutes at most.
I suspect the issue with the drafting job is that there's a time limit for the work in question, and OP won't conceivably be able to do it in Edinburgh if all the papers are in London.
I suspect all of us have travelled with a poorly child from time to time - I think for most parents the priority is to get the child home, and very few interrupt their journey to make the child stay in a Travel Lodge or similar.