Do you have purchased Windows installation files or installation disc as well as purchased serial number for Premiere Elements 12 your Windows computer?
If so, then open Premiere Elements 12 project to the Expert workspace, select Help Menu/Sign Out to Deactivate the program. Then close the program and next uninstall the program via the usual Control Panel route.
There can be unexpected Sign In failures after reinstall, but maybe not. The following are typical situations. No guarantees.
You may or may not encounter any problems with the reinstall and Sign In which should be with the antivirus and firewalls disabled.
Please let us know the outcome.