Can't access ARD client across internet

For starters, you're not looking at the correct ports. If you only have ports 5353, 5354 and 4500 open on your end, ARD will not work. ARD uses TCP 3283 and 5900, so you need to make sure that those ports are open and fowarded to the computer's internal address in the routers on each end.

Then you have to add the computer to the ARD computer list manually using the external-facing IP address of your brother's router. ARD will not discover a computer across the Internet by scanning unless you know the IP range.

More information can be found in page 53 of the ARD Administrator's Guide:

http://manuals.info.apple.com/en_US/ARD3.2_AdminGuide.pdf

Keeping an ARD connection working across the Internet can be difficult due to IP addresses that can change. You may wish to consider a more stable remote control solution such as LogMeIn which doesn't require keeping track of IP addresses or setting up a somewhat complex system to do it automatically such as DynDNS.

Hope this helps

You will need a static IP address from your brother's Internet provider as well. If you can get one, that will indeed make ARD much easier to deal with. Otherwise, the router's IP address can change, though it usually doesn't do so often.

Regards.