If you are publishing with the data sources embedded in the workbook, I do not think you can control the priority of each individual embedded data source, since the workbook as a whole is set to the refresh schedule.
What you would need to do is publish each data source individually to Tableau Online/Server, set each to a refresh schedule (it can be the same schedule if you like), and then modify the priority of when each published data source kicks off.
- http://onlinehelp.tableau.com/current/server/en-us/help.htm#task_prioritization.htm - Managing refresh priority on Tableau Server
- Manage Refresh Tasks - Managing refresh priority on Tableau Online
You can then modify your workbook to use the published versions of the data sources instead of embedding them in the workbook.
Thanks Lindy, I think that approach will work well. I rarely use published data sources so hadn't considered that solution.