Domain Access in 2 different locations

I’ve got a client who I support who travels between 2 towns say amsterdam and london. He uses a laptop WinXP Pro. The problem here is that the amsterdam and london offices are both indepentend domains. What I’d like is to have the amsterdam and london domain names appear as a dropdown at the login stage. But I can’t seem to be able to achieve that. When my client comes in from amsterdam to london, all you see in the drop down is local comnputer and amsterdam domain. To allow my client access the london network I’ve got to add his computer to the london domain. But then I loose the amsterdam domain!!!!
Same works vice-versa when he goes to amsterdam from london

CAN ANYONE HELP??