Would it be possible to board your animals while your brother is visiting? If I had the chance to spend time with a sibling that I didn't see very often, I would do whatever I could to maximize the time. If you boarded the animals and really cleaned before he got there, would that take care of the problem?
If he stays at a hotel, I don't think you should pay for it, but if he is coming over for meals during his stay, won't that set his allergies off if the animals are there?