Here is the setup:
1: I have one machine on a Domain called "MyDomain" this machine is
called "Hostmachine"
2: I have another machine in a workgroup called "MyWorkGroup" this
machine is called "GuestMachine"
3: Both machines are on the same network.

The problem:
I wish to write a sort of "proxy server" to be installed on
Hostmachine that can be reached by Guestmachine. This proxy server
needs to be able to handle any of the commands that Explorer (not IE)
can handle such as copy and paste and browse the network. The
restriction is that the Guestmachine has to use the Hostmachines
access to the network and not be queried for a logon\password. The
GuestMachine needs to appear to have all of the rights of Hostmachine
on the network. There can be no changes to the network as it is
configured now.

What I need to know is how to go about this. Are there API's that I
can use? Do I need to install a piece of software on the Guestmachine
that acts like a debugger and intercepts a special command to Explorer
so it can browse the network through Hostmachine without interfereing
with browsing the local machine?

If there is a piece of software already out there that handles this
then this would be acceptable.

Is it possible to use something like VNC or PCAnywhere to perform your tasks?