There are a lot of activities that happen with the regular Kentico C# API that I'm not sure the REST API handles OOTB. Simply dumping the order and order items into the database tables, doesn't automatically trigger any of the other necessary API calls needed to perform the proper results for your application.
What I'd suggest is create a custom endpoint that simply takes an order object with items and inside that custom endpoint, you perform the actions via the Kentico C# API to do your work. I think you'll have a much better result than if you were to continue to force the REST API to do the work it can't.