Two routers, two different SSIDs, one modem?

I'm looking to set up two separate home networks; I know how to change the router address to a "2" to have a separate network for login, but is the rest of the setup as simple? It looks to me like as long as I use splitters for the various ethernet cables to and from the modem/routers then I should be fine, is this correct?

For example: Modem is connected to router 1 with an ethernet cable, would all I have to do is split this connection and connect it to router 2 to get it working?
 
Still might be able to do something.

In my case I do not allow sharing and have several systems - each on its own with Public WiFi protections in place: Firewall enabled, Secure connection, Antivirus

All this is behind a router which provides NAT firewall

If I had one system which I wanted to protect I might try connecting second router WAN port to one of the regular LAN ports on the first router. Then connect the 'safe' system to a LAN port on that second router.

Glad to hear any objections, criticisms and comments - I just hope it isn't as bad an idea as drinking bleach.
 
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