This is not Adobe. Rather user to user. And, the nature of your question lends itself to "the only by Adobe resolution". But, here are my comments for your consideration.
Adobe allows for the same purchased activated serial number on no more than 2 of your computers. And these two are not be run at the same time.
Program activation and registration are not the same thing. In recent versions, registration is done automatically with the Sign In with the Adobe ID and Password and program activation.
If you are dealing with the program being registered to the IT people with its Adobe ID and Password and not your daughter's, then check out the Adobe transfer of license details. Adobe is the only one to handle this aspect of the matter.
If this is not a matter of IT using its own Adobe ID and Passwood.....
When you open the re-imaged laptop and go to Control Panel/Installed Program do you find any trace of Premiere Elements 11 there?
If not, I would go ahead and install Premiere Elements 11, presumably from your installation disc and using the purchased serial number and your daughter's Adobe accepted Adobe ID and Password.