We do distribution, and have inventory, but the process we use for drop ships should be similar. We create the Sales Order, and in the Sale order line, we have a Drop Ship site, and a "Linked PO" field, (new as of late last year) where we tie the PO to the Vendor.
We too, receive an invoice from the Vendor, which we Receive into the Drop Ship Site. Then we will create an Invoice (Create invoice in the Sales Order toolbar) from the Sales Order, which "Ships" the material from the Drop Ship site and invoices the customer. The Customer pays our Invoice.
We'll pay the Vendor invoice separately, and never "pass along" the Vendor invoice to the Customer.
To see what Sales Orders are still open, you can run a report in the Sales area of Reports, "Open Sales Order Report by Customer" which will show Uninvoiced Sales Orders.