We have family who simply do not visit us because we have cats, or stay mostly in our cat free office space most of the time.
Agreeing with previous poster, changing to our Dyson vacuum made a HUGE difference in the amount of cat hair (and dust!) everywhere. It cleans it off our furniture significantly better as well. We used to get the $80 vacuums because that is what we could afford at the time. I would request, and personally clean his sleeping space and keep the cats OUT.
Zyrtec, Benadryl, Flonase nasal spray, Zatidor eye drops, real Sudafed, saline nasal rinse (neti pot is what we use but any is fine) will all help since you are stuck playing there. Showers in morning and at bedtime, middle of day if needed too.