iChat has some bugs
iChat also has some new bugs. I experienced them on Video chat, exactly as you described. I was able to work around it by simplifying my routing configuration. Screen share, however, was impossible to get working in the same configuration. My configuration involves a PPTP VPN connection, with some destinations not going through the VPN, and having internal IP addresses.
A network trace confirmed it was a bug; nothing to do with your network capacity.
edit: Oh, and don't connect to the wifi AND the cable. Try just one at a time, and make sure to quit and restart ichat each time you switch.