Just go to tableau server in web and view your data source 2 and check the permissions settings for those users. I guess you have given "denied" privilege for those users on data source 2 to view/download/edit data source. Just give access to them. I hope this can resolve your issue. Let me know If this help.
Both data sources have the same permissions on them.
Any other ideas?
Can you send me the screen shot of your permission setting for those user for each data source?