Taoyuan (CKS) Airport stopover - help please

My parents will fly with China Airlines Phuket>Taipei>Frankfurt. Arrival time in Taipei at 11 pm, ongoing flight departs 11.10 pm, so a connection obviously not possible. China Airlines refuse to pay an overnight stay, as parents have a stopover already in Taiwan on the way to Phuket.
So where can my parents have a decent stay around CKS or Taoyuan ?? Trip to Taipei not advisable as they just wanna find a quick bed…Place should be clean and in the middle of some action, as they must entertain themselves until 8 pm the next day to get to CKS to catch the next FRA-flight…

Doing this, is that regarded as a second official stopover in Taiwan? They will stay less than 24 hours and only due to the flight schedule…Would it make sense to insist CI to pay for the night?? The office in Germany said no, but here in Taiwan??

Last q:
Can my parents still check their baggage in Phuket through to Frankfurt and just leave CKS with hand-baggage??

I know the last questions the CI office can give me the answers as well, but I just wanna know if someone in here already made an experience like that before??

Thank you

There is nothing entertaining around CKS Airport. Best thing to do would be to take a cab to Taipei and spend the day there.

You should just send them to Taibei. Hanging around the airport hotel until 8PM would be incredibly dull. Taibei is an hour bus ride away while Taoyuan is a half-hour taxi ride away.