You'll love my answer here ;-}
It depends on the Router You have two different directions you could try to set things up.
A double firewall: your PC > Router^1 > Router^2 > Internet (where ^ implies other ports for other wired or WiFi devices.
This setup can create problems as you could have two WiFi networks that you could connect into and depending on what you needed to access you may not be able to connect as the firewall function will block you. If you disabled the Router2 WiFi: your PC > Router^1 > Router2 > Internet - Then you should be OK.
The other choice is setting one of the devices as a filtering Bridge for the upstream Router. The problem here is not all routers offer Bridging. Without getting to deep here if you review the ISO/OSI networking model Bridging is a layer 2 function were Routing is a Layer 3 function.
So in your case: your PC > Router^1 > Bridging/Router^2 > Internet - Here the devices connecting directly on the Router or Bridging Router BRouter are protected but the circuit between the Router and the BRouter is set up as a bridge connection so any connections off of it are managed on the upstream Router (down stream is the internet).
Lastly, some Routers just don't play well with each other. Make sure you have the latest firmware on both and talk with the support staff for both devices on how to set things up. Between the two of them they should be able to tell you what can or can't be done. Hint Don't tell them you have someone else's unit, say you have two of the same devices. Then merge in your notes the two answers to figure-out how to setup your units. If it doesn't work then call them back and this time tell them what the other devices is (often they will wash their hands of helping you if you tell them you have different devices).