Deploying Premiere Elements over a network is a very challenging process, Kathy. The program isn't made to work or to be used over networks, and I highly recommend you contact Adobe tech support directly and ask them for advice.
We often see posts on this forum from teachers who've tried to do it and, without the proper set-up, it usually won't go.
As Steve points out, similar academic questions come up fairly often. The problems that the professors usually encounter are with permissions and the log-in for the students over a networked environment. We all understand the reasons for wanting to limit the students with their programs, but PrE (and PrPro) are designed as stand-alones. This creates a series of problems in a lab situation.
Adobe TS, or Customer Support, should be able to give you the criteria for getting as close to what you need, as is possible.
I have a humble request for you: please report what you find out, and post that info back here. Since we are individual users, we do not encounter the situation that you face, so we really do not have much info on how to implement the needs that you have. Your posting back will help us to then help teachers in the future. It will also give us the info to link to for the next teacher in your position. Please help us to help the next teacher with a similar problem.
Thanks and good luck,