Please try to have your daughters cats ride with her as her carry-on. I heard a statistic that animals carried in cargo have a 1 in 4 fatality rate. ONE IN FOUR! It is criminal.
Ugh...travel by airplane, especially long term, can be hard on any cat/animal, especially a sick one.
Have you contacted the proper authorities (U.S. in this case, especially) yet about requirements for travel carry cases as well as the possibility of kitty having to be put in quarantine? Shots, vet papers, etc...?
I'm not totally up on the recent rules for importing domestic animals (been over a decade since i had to deal with it) but I understand they are even stricter than they were before.
If you haven't checked on this, do this ASAP. The proper paperwork, authorization, etc...can take months to obtain, depending on the situation.
Otherwise, the trip and possible quarantine is the big issue. I'd say find out what your looking at, and then decide what you'll do. Once situated in a new home here in the U.S. kitty should be fine (as long as our long standing republican regime doesn't upset kitty's political sensibilities!!! :)
Is this a case of kitty having to travel in the under carriage, or do they have some sort of arrangement now for cats to travel with passengers? With a 20 hour flight, medicating kitty is likely out of the question, especially if you won't have access.