Duplicate the tables and update/append via queries linked to the odbc tables? If you're only using some of the fields from the odbc side, start with a make table query and have the native table only contain the fields you need.
As for daily updating, my preferred method was to use windows task scheduler. I had it open the db using a command line switch in a shortcut and the update code knew if it was a user or pc that was opening the db. If pc, code execution was direct and didn't present any messages that couldn't be dealt with, or worry about anyone being logged in because the update ran at 4:00 AM.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.