Kellie's Dad,
Wow, that's a tall order for a small mixer that you also want to use for live sound. I think what you need is a mixer that supports automation, and its likely to be *very* expensive. So much so that I've never even looked for one.
Even so, I think that mix automation only applies to the faders. I'm not sure if automated analog mixers also automate panning, effects sends, EQ, etc.
There are control surfaces- hardware that looks like a mixer but just changes the settings in a software mixer- but they are no good for live sound. There are digital mixers that can save and restore mixer scenes, but they aren't for live sound either.
I've never heard of an analog mixer that was able to show adjustments on a computer screen. Hopefully someone else will be along shortly who does know of one. I'm sure it would be unearthly expensive, but it would be neat to research how it works.
Chris