Is this a case where those tedious performance reviews and objectives are useful? If you are meeting your objectives no one can complain and if not there appear to be good reasons why not and presumably you can raise these in the regular meetings I hope you have with your boss? And of course note dependencies, like colleagues who pull their weight, in your performance review. It never hurts to gather data to support your case, and facts/figures might help you make a case for, say, a temp to help with admin, training for your inadequate colleagues, you get the picture I expect.

I presume your boss and indeed her/his boss would be equally mortified by an inspection failure so one would hope they would work with you on this? Of course many bosses are lamentable and best left to their own boiling.

Just some thoughts - I still think you deserve a medal. Children cannot be expected to know better, but parents are even worse than their noisome spawn.