I do not understand what it is you are trying to achieve. What do you want to accomplish and why do think using two different subnets on home routers will do it?
The normal way multiple (home) routers are interconnected is to disable DHCP on all but one of them and (2) to put them all on the same subnet. Why? So that you won't have the conflict of both routers attempting to assign a different IP address for their subnet at the same time.
The other potential problem I see is that you have NAT enabled on both boxes. Why? Only 1 of the routers should be connected to the Internet and that is the one that needs to have NAT enabled. The other is basically just functioning as a switch and possible as a Wireless Access Point (WAP). You don't want to be NATing on top of NAT.
Maybe the info in this article will be of use to you.
Some additional thoughts:
I want to be able to connect to both routers independently
I wasn't clear on what you meant by that when I wrote the above. Looking at it again I'm wondering if you meant that you want to be able to connect wirelessly via either router. In other words, add one of the routers to the network of the other router as a another Wireless Access Point in the same wireless network.
If that's what you're trying to do then perhaps this article on how to add another WAP will help.
FWIW, the idea behind subnets is to provide a simple way to route packets. When using the Internet Protocol (IP), the first thing a device must do before sending a packet is decide whether or not the destination computer is on the same physical network or on a different/external network. In other words, can the packet be sent directly to the other computer on the local ethernet or does it need to be sent to a router to be resent to a physically external/different network.
If the destination IP is on the same subnet as the sending device, then the sender looks up the ethernet MAC address of the destination and then sends the IP packet directly on the local ethernet. If the destination IP is not in the same subnet as the sender, then the packet is sent to the router which tries to forward it to the destination network.
The home networks I'm familiar with are logically one physical ethernet network. All the devices should be able to talk directly to each other. So all the devices on a home network should be placed within the same subnetwork.