When my client inserts an order manually via VM Invoice, is there a way for it to send the full order details in the (pending) email, rather than just the order status?

It currently sends the status email with a link to view the order details ... which then requires the customer to login (and they obviously don't have a username and password).

Is there a workaround, or a configuration option that we've missed?

Thanks for pointing, that feature is not presented yet. It was added to your to-do list. But we can't tell you when this will implemented, because we have a lot of tasks now.

UPDATE: This resend-feature is available in VirtueMart (i think from version 1.1.5) in order view.