Since Windows 7, members of Power User have no more user rights or permissions than a standard user account. In your scenario, in order to make the check-in software retaining its printer configuration, add user into Administrator group for test.
If still no help, it means your software has some compatibility issue with Assigned access in kiosk mode.
You know, Assigned access is a feature that allows you to create a lockdown environment that lets users interact with only one app when they sign into a specified account. With Assigned access, users won't be able to get to the desktop, Start menu, or any other app, including the Settings app. Based on this prerequisite, your check-in software may have the different behave.
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