Got a child or a bunch of child like adults.
AppleCare +
AppleCare+ for iPad extends your coverage to two years from the original purchase date of your iPad and adds up to two incidents of accidental damage coverage, each subject to a $49 service fee.
An out of warranty iPad mini is about the cost of a new one. Double that or more, depending on configuration, of the cost of AppleCare+ and the service fee.
If you manage to trash it again, its only $49 for another one.
For you AMEX will fix it folks.
If you drop it or the screen cracks Apple will call that ACCIDENTAL damage on the repair or out of warranty replacement Receipt.
AMEX WILL ONLY COVER ACCIDENT DAMAGE FOR AN INITIAL 90 DAYS.
The term SOL comes to mind.