Only the training program and the MD that is supervising the resident can bill for a resident's services using modifier GC. It sounds like your clinic is private and not part of a training program, so you won't be able to bill this way.
I don't see any way that you could legally or ethically bill a medical resident's services under an ND's NPI. These are two different provider types - they can't represent that they are performing each other's services. My suggestion is that you get the resident credentialed with the payers whose patients you want them to see and bill their services under their own credentials. If you are billing one provider's services under another provider's credentials and not billing 'incident to' (which doesn't apply here since the resident is not a mid-level provider), then you would be potentially filing false claims. You could try contacting the individual payers and ask them for written authorization to bill a resident's services under the ND, though my guess is they would not allow this.