... These apps haven't been accessed since the day they were downloaded. This is all verifiable, but the rep insists they're "legimate" charges, and is not prepared to waive the nearly $100 we've been charged for the dowloads and what is now 2 months of subscription fees. ...
First, unsubscribe to the apps - cancel, stop, delete, whatever....to stop the monthly charges. Then, see if MAYBE Verizon will backdate a data plan for the month the apps were downloaded to cover that expense (too much time may have passed) and possibly refund the second month of app subscriptions if you in fact did not use them. No guarantees, but given your situation, they may be willing to give you some of the above concessions.
If not, consider it an expensive lesson, block data on the phone if your nephew is anywhere near it, and move on.