Connect one computer to two routers

Hi,
I have a question which hopefully you can answer.

Router/Modem one is attached to the internet and transmits a wireless signal. My computer is connected to the internet via a wireless adapter, when I want to connect to my network TV HDD, printer , and home server (possibly a windows home server in the future) I just disconnect from Router one and connect to Router two. I want to know if it is possible to run a wired Ethernet cable in-between my computer and router two so I can connect to both networks. Wired to router two with the HDD and printer, and wireless to router one for internet.
Now here are the rules!!!

-I can NOT run a wire in-between router one and router two (by order of wife!)
-I can disable the wireless and/or DHCP on router two or even replace it with a switch.

If you have any good answers I would really appreciate them.
Thanks a lot,

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