Using 2 Time Capsules on same network but on "opposite sides" of router

If the Netgear device really is a "simple" modem......not a modem/router.......then TC1 must connect to the modem and everything else on the network must connect to TC1.......as shown in your first network diagram. Any other routers that connect to TC1 must be set up in Bridge Mode.

So what I'm trying to do is this:

If R really is a modem/router, then both of the TCs need to be set up in Bridge Mode if this is your desired configuration just above. Another way to say the same thing.......both TCs need to be "downstream" from the modem/router. In the correct setup, your modem/router will be doing DHCP and NAT, so it will be "in charge" of the entire network.

It might be another discussion, but in your current setup with one TC doing DHCP and NAT, you have what is known as a Double NAT error on the network, since both the modem/router and the TC are doing NAT. The current setup "works" because all of your network devices are "downstream" from TC1 and Double NAT is usually not too serious of an error on a simple network.

If it helps, you do have the option of connecting an Ethernet switch to one of the LAN <--> Ethernet ports on TC1, and then connecting TC2 and other devices to the switch.

Or, connecting TC2 to the switch, and then connecting other Ethernet devices to an Ethernet port on TC2.

For example, my main AirPort router is in the office next to the modem. I have run a 40-50 foot Ethernet cable from the main router to another main area in the home and connected a switch at that location. A second AirPort connects to the switch, as well as other Ethernet devices.