Questions:
- How are the users running the logon script? (How is the logon script getting started?)
- Why are the users not logging into the domain?
- Are the PCs part of the domain?

This is not an impersonation problem, but more that Ingroup will not work the way you are trying to use it. There may be another way, but the only way I can see you getting this to work with ingroup, is to create a local group on each pc called Supervisors, and stick the user in it.