Double RDP session - single login/logout

Assume I want to have a person login remotely via RDP to a specific single computer - computer A - on a network and then from that computer login via RDP to a TS server - TS1 - but make it so that they only have to present their credentials the first time on computer A and then automatically be logged in to the TS session with the same credentials. Please note that I know about being able to log directly into a Terminal server so I don't need any information on that - I am aware that what I am doing is a double-step process but I have my reasons.  As it stands now I have this working so that the remote user RDP/logs in to computer A and then gets an automatic prompt to log into TS1 and all is good except for the little irritation of the double login. Logging out requires a double logout as well. If possible I would like it so they enter their login info once in the process and then only have to do one logout as well.

Again, I know fully well that it is possible to log directly in to the TS without the intermediate step but again I have my reasons for seeing if things can be done the way I've described.

Home user is using XP, first computer they log in to is XP, server is Windows 2000.