WiFi vs Wired

I have a Netgear 4 port wireless router in my living room. It's hard wired to the DSL Modem/main Router which is also wireless. The signal is weak between the two routers. If I connect to the network using a wireless adapter in the living room, is the information sent via the wire or is it sent using the wireless portion of the router because that's the way it was received?

You are connecting to your Netgear via WiFi (assuming you are connecting to it). It will connect to your DSL modem via the cable.

I would try to disable the DSL modem WiFi, if your not using it... it's just a security risk.