User needs to email invoices to clients with separate client admins.

You can do the following:

1. Create a client contact with two email addresses (one for client and one for admin).
2. Assign this client contact for billing at the project level and select the option to send the invoices to the project billing contact. 
3. When emailing invoices, use the Client Contact option from the Email menu. Both emails should appear on the Compose Email screen.