Does work vpn compromise home privacy & security?

I work for a snooping kind of company where I would not put it past
them to watch what I do on my personal home computer if they could.

Can they "see" what I do on my home laptop when I vpn from home on my
work laptop?

Often I am asked by my manager to use Nortel VPN to connect to the
work network using my home ISP on my work-owned portable Windows XP
laptop. At the same time, I am on my home WinXP PC connecting through
the same Linksys wireless router.

I'm pretty sure when I do not VPN in from the work computer, they
can't "see" what I do on the home computer ..... but when I vpn in on
the work computer on the same network as the home computer .. .... can
they "see" what I do on the home computer?

Does VPN compromise my home security or is my home PC activity still
secure?