You don't give nearly enough detail or any really so no one can answer this. Are you "using their" 501c3 so that donors to you can deduct donations? Otherwise if you have a not for profit corporation or entity you can still operate, but your donors can't deduct their donations (although your status may end up being retroactive). I would also be concerned about transparency with the people you are dealing with - both outside and between the two organizations. The bottom line is there are a lot of questions and you need specific legal advice you cannot get here.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.
What you are describing is a potential "fiscal sponsorship" relationship between your program/entity and an existing 501(c)(3) charity. This is completely legal as long as it's done correctly to ensure compliance with IRS provisions. I suggest contacting an exempt organization's attorney well-versed in fiscal sponsorship for nonprofit, exempt organizations.
The information that has been provided on this website, including information contained in any link or informational reference, does not – and shall not be considered to – constitute legal or professional advice. The reader should not consider such information to be an invitation for an attorney-client relationship, should neither act nor rely on such information, and should always seek the advice of competent counsel licensed in the reader's state. Attorneys with the For Purpose Law Group are generally licensed to practice law only in the State of California. The ability of the reader to access this website in another jurisdiction does not constitute the practice of law outside of California, or a representation that members of the For Purpose Law Group are licensed to practice in any other jurisdiction. This site is not intended to, nor does it establish an attorney / client relationship between you and this office.