Hi,
firstly, every policy has subtle differences, so you really should contact the insurance company, but from my experience...
Your parents will probably only be covered for loss of their deposit (less excesses), if they need to cancel their trip due to your niece falling ill as she has fallen ill before the balance is due to be paid, again they should contact the insurance company before paying the balance.
There is probably a clause n the insurance stating something like... cover would not be provided if your niece was hospitalised during the last year, or if the illness is related in any way to a pre-existing medical condition.
I have never worked with claims myself, so unfortunately can't help you with the turn around time.