I can not see the situations as analogous.

Charles Musgrove is the head of the house, Mary is completely inept, and Louisa's health is at stake. I do not care if she throws a flying fit, she can not actually stand against Charles if he puts his oh-so-masculine foot down, and says, 'go.' It will be uncomfortable for him, because, apparently he has never done this before (really? how wierd is THAT?!?!?), but with Louisa's injury so dangerous, he should suck it up and deal with the discomfort.

Of course, Mary should deal better with her disappointment at not being actually useful, too. If we are to believe that Louisa is truly balancing on the knife's edge between recovery and death or disablement, they both drop massively in my estimation when they let their own selfishness interfere with her best chances.