Remote desktop allows you log on to a remote computer. What your brother can do is send you a remote assistance request. You can find how to do it in Help. I dont believe that he will be able to see what you are doing because Remote Desktop establishes a different session other than what you brother is using.
You would need a program like PC Anywhere or a like program. A program that is free to use that is like PC Anywhere is VNC. You can download the free VNC client at http://www.vnc.com. Install the server portion on your brothers machine and install the client portion on your machine. When you execute the client it will prompt your for a computer name or IP. Alternatively you can setup the server part where you have to provide a password.
On note though is that this technology is not secure. I recommend you doing this over a secure tunnel.