MySQL Slave Relay Logging but not logging Binary Log
You forgot one thing
binlog-do-db=our_database  
binlog-ignore-db=mysql  
binlog-ignore-db=test  
replicate-do-db=our_database  
log-slave-updates

The option log-slave-updates takes SQL that was read from relay logs and records them in the Slave Binary Logs when the SQL is completed.
Please be very careful. You should never use binlog-do-db and binlog-ignore-db simultaneously. I wrote about this back on Jun 14, 2012 ( Configured MySQL replication but its not working ) which points to an old Percona article on binlog-do-db being dangerous.
SUGGESTION
Of the things you are using, you only need these lines
replicate-do-db=our_database  
log-slave-updates

You really don't need binlog-do-db=our_database once you have log-slave-updates working properly.