You have basically created a stored value and money transmitter business without the proper license. In addition, you've created a conduit for criminals to launder money.
See:
* Liberty Reserve - https://www.justice.gov/opa/pr/founder-liberty-reserve-plead...
* Ripple - http://www.americanbanker.com/news/bank-technology/fincen-fi...
* FinCen MSB fines list - https://www.fincen.gov/news_room/ea/
Disrupting finance is hard for a reason.
The rule is simple - if you take and hold on to customer funds, you need to be licensed for money transfer in all the states you operate in.
Today, a few services like Braintree and Stripe offer a middle ground solution. Essentially, they will open an escrow account for your merchant customers, and you move any money your holding into the escrow. They will then hold the funds until you release them. This approach is clever, but still a legal grey area.
If you're a marketplace startup, focus on your customers and your startup and outsource the highly regulated parts to third parties.
1) Parents are charged via typical merchant mechanism to fill their account with "credits" worth $0.99 each, costing $1.00, and can optionally allow the app to automatically top-up their account when low.
2) The service sends cash in a registered mail envelope at a frequency configurable by users, with mailing fees paid for by credits.
Then the business can function and grow a user-base, and by holding the balance, the company can build up a lot of cash-on-hand which will enable them move onto the bank integration they originally wanted. Bonus: receiving legitimate mail and getting cash in hand are very exciting experiences for a kid.