Sorry, but it is not possible to add the Group Policy Editor to the Home versions of Vista. This tool is only available on the Business and Ultimate versions. However, some (but not all) of the changes that can be made with this editor can also be made by editing the registry directly. In other words, it is a bit like an interface centre. Those changes which cannot be made this way refer to the features of Vista that are only found in the Business and Ultimate versions.
There are limitations to the use and functionality of 'Remote Desktop' (RD) according to the version of Vista (and, in your case, XP) that you are using.
The computer that you want to control - the one at the remote location - is called, unsurprisingly, the remote computer. The computer you want to use to control the remote computer is called the client computer.
For the remote computer, you need to be running either Vista Business or Ultimate as the Home editions do not include the required components for hosting RD sessions. The remote computer can also use XP Professional.
On the client side, you can access RD from a computer running any 32-bit or 64-bit version of Windows. This computer must have access to the remote computer via a network connection, virtual private network, or dial-up connection.
The section above about the remote computer explains your problem - the Home editions of Windows Vista and XP don't have the necessary components for hosting RD sessions. This is because it is classed as a Business tool.