Q: how can I cancel an order my granddaughter put in without my knowledge

Purchases are considered final, but you can try the 'report a problem' link to contact iTunes Support and see if they will refund or credit you : http://reportaproblem.apple.com

If the 'report a problem' link doesn't work then you can try contacting iTunes Support via this page : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption

If it was done on an iOS device then to try and stop it happening again you can use Settings > General > Restrictions on it to turn off in-app purchases and to require your password to be entered for every download