Yes, your prerequisites sound just like mine (we're busy moms with very MOBILE CHILDREN!). I wrote practically your exact same post a couple of weeks ago. And since then, I've learned countless bits of information about zoom, image stabilization and why weDON'T need a super-duper 7 megapixel camera!
Didn't realize (like lots of people) that determining MP need is based mainly on howbig you plan on enlarging. Since I'm also mainly going to be needing 4x6's and an occasional 5x7 or 8x10 then: 3-4 MP is plenty. I also learned that with having kids, an ultrazoom camera is a must (gotta get my 3 yr old in her ballet recitals!)... along with having image stabilization (why the Kodak DX7590 with 10x optical zoom doesn't have I.S. is beyond me!). And another thing: I've read countless times that just because a camera has a lot of MP doesn't make it a great camera if its got a crappy lense (which thePanasonic FZ's do not).
So, I've compared a lot of them in the 3-4 MP range with 6x-12x optical zoom (Canon S1 IS, Fuji S3100, Minolta Z2/Z3, Panasonic FZ3 - just to name a few).
The scales definitely tilt toward the FZ3. Do you live in Knoxville? We do... I know they've got them at the Circuit City near Cedar Bluff. Go check it out... put it in your hands and see how it feels. I think when we order ours, I'm definitely ordering online: Circuit City has the FZ3 for $399 (not including our outrageous sales tax here). But you can getit atseveral places online for around $315 shipped to your door.
Here's a link to some FZ pics from users here:
Good luck! :-)