FIRST, check with the Tax Accountant!! Does the new Sub actually have Non-Profit status with the IRS?
You can't just give someone non-profit status just by running the money through another non-profit. IRS will go after both for the taxes and penalties and the Primary Company will probably loose their Non-Profit status.
Having said that... It's still a question for the Tax Accountant because they need to show it properly when reporting. But since you said the money isn't yours, but the Subs, my guess is that you'll just set up a Other or Long Term Liability Account for the Sub and show all money going in and out of that account.
So a Donations collected that go into your Checking would be applied to this Liability Acct, then the Payments you make (monthly, weekly, whatever) will also be applied to this Acct to show the money coming out of this account and going to the Sub.
Any Fees you may be charging for this service would also come out of the Liability Acct and probably have to be shown as income to the Primary. But again, a question for the Tax Accountant.