First of all, which router? Second of all, it is possible that the masterserver files are different, or that Steam picks a different port to contact the masterserver it chooses from one machine to the other. Also if you are playing at the same time on the same server, you sometimes have to change the Steam clientport, at least for some Valve games, or there is a conflict with data trying to be passed on the same port, which can only be forwarded to one machine at a time. No idea if this holds true for RO2.
If you do have a known troublesome router and you want to see what is going on, download Wireshark and start a capture on both computers, and run this filter: udp.port==27010 || udp.port==27011
If you don't display any results in this Wireshark log when refreshing the game list, but your son's PC does, then his connection is triggering the faulty rule. Also, if you've replaced the files on both machines, but he is using either favourites or recently played tabs to join, then that for some reason also triggers a connection on one of the ports.