[Amnesia]

I don't think a wireless router works the way you want for the second router. That is, it can't be used as a wireless bridge.

In any case, for the second unit, you don't want a router at all. A router is designed to "route" IP request to different networks. You just want to use the second unit as a switch---that is, to send signals within a given network.

Networks are complicated enough without usuing inappropriate hardware...you want a bridge like this.

 

[Amnesia]

In order for me to wirelessly network an S3, I can only use the TiVo brand wireless adapter?

No, that's not true. I used to use a Linksys USB adapter. IIRC, the series 3 supports the same adapters as does the Series 2...