I have a direct line cable internet connection for my PC and I'm using
Trend Micro PC cillin and all it's security options for my protection.
Now... my wife's PC is using a wireless signal from a Linksys router
from my machine.  My question is this:  Does she need to install the
Trend Micro Software on her PC also or is she covered by mine?  make
sense?

Thanks in advance

Based on what you're describing, She'll need her own security software
to protect her computer. Her internet connection is from her computer,
to the router to the internet. Yours is the same, just the medium to
the router is different (hard-wired vs wireless). Because she is not
going directly through your computer, your security software does not
protect her machine.

-JtB

Yes, she needs to install Trend Micro Software on her PC. Both are accessing
the internet via the router through different medium.