Best answer by ratty
If you reset the Beam and added it when attached to the primary router it would become part of the main household, and inherit all the settings/accounts therefrom. However the moment you move it back to the second router it will become detached again. Any changes made on the main household won't be reflected on the Beam, and vice versa.
Sonos devices and controllers must sit on the same subnet. They can't communicate between subnets. The Beam won't see or sync with the main household because you have the second router in between.
You really should simply configure the second router in 'bridge'/'access point' mode (many newer routers have this as a config option) then all your Sonos units will be able to communicate with one another.