I found the integration piece for RMH with QuickBooks at the following website located here. I would contact them to see if it is a service they already offer.
Also, you might look into the following app on QBO if that doesn't work: Hike - POS Software, Retail Management, Inventory and see if it will integrate with your RMH system already? It's worth a shot.
Also, Your invoices = Income and your Vendors = Expense and/or COGS. If neither of these things work, I would see if you can hire someone to take your reports and turn them into a Journal Entry that can be posted into QBO for you. If you need any help, I would love to help with that.