Cascading routers: accessing secondary router's clients from first router?

Sounds like you know a bit about networking. Good job on the explanation.

However, you have failed to consider that the router is a security barrier also using NAT and possibly a firewall.

For the same reason devices on the internet can't access Router A clients, devices in front of Router B can't access Router B clients.

Specifically, the problem is NAT. We could get in to some gory details about how advanced routers don't actually need to NAT and NAT rules can be adjusted. But, I'm assuming these are just home routers with limited options.

Therefore, your only option is probably to turn on port forwarding so that you can access a specific port on a specific machine on the B side from the "dark side" also know as Router A clients. :)

In addition, Router B probably has an option to drop or ignore PING (ICMP packets) on its WAN interface. Therefore you cannot ping it from Router A.

I'm sure you have your reasons for this setup, but it sounds like a simple switch would be better utilized in place of Router B. You can also disable DHCP on Router B, plug the cable in Router B's WAN port into a LAN port on Router B and it too will be a simple switch. You might also want to reprogram Router B to have a LAN IP that is on 192.168.1.x so that you can still reach the configuration interface after doing this.