Well, it's your family, so legally speaking you are allowed to mess with the network. You don't actually need to use aircrack or anything, just use an ethernet cable, plug it in the router, and the other side into your computer, and you should be able to a/ access the network, b/ change the password to the wireless network.

If he's password protected stuff, just reset it (there should be a little button allowing you to reset the thing). Just set a password of your own, and DON'T FORGET TO ALSO USE A PASSWORD ON THE WIRELESS NETWORK, USING WPA. Then, kindly help everyone in the family getting back on the network.

He probably installed a trojan horse, keyloggers or whatnot. Unless he knows one password, he can't just detect other passwords, even with full control over the router. Change your passwords, every single one of them, and do it at a friend's house, on his computer (don't use yours).

Install AVG, or Avast, also run Spybot S&D. Install a firewall, and look at every application that attempts to connect to the internet. Only allow things that you explicitly want to access the internet (or worse, a local IP).

If you want, install Linux on your computer. With encrypted partitions. Use a strong password, and don't disclose it.

You can win this without playing dirty. You have a right to use the internet, you have a right to privacy. Depending on where you live, those are constitutional rights.

If you want to get your mum on your side again (and this one may be a dirty trick), tell her in private, late one night, that you think you need to go talk to someone because your brother gives you suicidal thoughts. I know, risky, and hardcore, but it could get your brother into heaps of ****.