If all you have is the Premiere Elements 13 purchased activated serial number on one Windows computer, you can go ahead and do nothing else but install the program from the disc on the second Windows computer with the same purchased serial number.
That will leave you with the purchased activated serial number on two of your computers.
Adobe allows you the same purchased activated serial number on no more than 2 of your computers. So, nothing to do but to use one at a time.
Lots of scenarios beyond.
1. Deactivate Premiere Elements 13 from computer 1. Do not bother to uninstall. Deactivation is not the same as uninstall.
To deactivate, in an opened Premiere Elements 13 project, go to Help Menu/Sign Out. Close out of there.
Then do nothing, leave the program in the deactivated/installed state.
2. Deactivate and Uninstall Premiere Elements 13 from computer 1.
Any questions or need clarification, please let us know.