Sick child etiquette. Would you be annoyed?

Pay for a hotel if you don't like it. Being sick isn't something you can stop if you try really hard, and if she doesn't want to cancel a trip a day before and not get her money back or leave her child with a SITTER for a FEW DAYS! then that's good. Of course she doesn't. It's not her fault, so if it bothers you, sort it out yourself by staying in a hotel.