You need the driver for your home printer to be available at the Terminal
Server.
In addition, the port by which your printer attaches to your home machine
needs to be one which is redirected by Remote Desktop Connection software.
Neither of these is perfectly simple, unfortunately.
You need a robust, well-designed printer driver which is signed by
Microsoft's WHQL (Windows Hardware Quality Labs) in order to help assure the
server admins that this driver won't cause instability of the server. This
is a real issue, and they may well be reluctant.
You can look at properties of the home printer, ports tab, and see what port
is used.
If it is LPTx, COMx, or USBxxx, you should be fine. If it is DOT4x(xx?)
then there may be difficulties, and I can't guarantee the result:
http://support.microsoft.com/?kbid=302361
making the registry change in this article, restarting the PC, and having
the driver available at the server MAY work, or it may not.
Let us know what printer and what port, and we can give a better idea of
your chances--might ask the folks who run the Terminal server as well.