Home most likely doesn't support Remote Desktoping another computer.
All versions of Vista support outgoing RDP connections. Vista Home Premium in theory won't act as an RDP server for incoming connections, but in reality requires a minor bit of legal hacking to function as one. It would be unsupported by MS, however.
The OP's situation seems to be an outgoing connection to an XP pro box which should work fine with an updated client. Please follow up if that doesn't work, or if you need to run the laptop as an RDP server.