FYI: E-mail Support suggested I try connecting a different computer, after they were unable to duplicate my issue. I have, and that computer is connecting perfectly. No issues, the bridge is functioning just as it should - I waited several days with sleep times of ~10 hours to be sure before I updated.
The moral? Make sure you have a separate computer for your children to use, preferably on a different network in another country... And don't try to connect it behind an OBi device. It might be better this way, they may have ended up somehow infecting it with their 'anti-computer' disease in the future...
Thanks everyone for your help, comments and most of all patience.