I added Spybot Search and Destroy to my anti-spyware arsenal last night, now how do I get the Resident to run in both my account and my parent's account?

You can either install it on both accounts or have a look through the registry and see what it loads under the run section.
Of there is something there then copy it over to your Parents account

That is strange, I don't see an entry in any of the Run, RunOnce, and RunServices keys. I will just install it in my parent's account when I get some spare time.

When you install it, it should be

C:\Program Files\Spybot Search & Destroy

It will then be accessable to everyone.

If you just want to install it so only you can access it, i will give an example. If i was installing it so that only i can access it i would install it to:

C:\Documents And Settings\Wayne Austin\Spybot Search & Destroy

I have installed it to be accessible to both users, but S&D Resident only runs in my acount, and I want it to run in both.