I had a Lunix FZ 18 and it actually took great pictures. But when I saw the photos my brother took with his Nikon D40 of his son, I was sold on getting my first DSLR. I have no regrets getting the D3100. I've taken some great shots of the kids that I otherwise wouldn't have been able to get with the FZ 18.
But you're right, lugging expensive camera equipment and chasing kids do not go hand in hand. In fact, I broke the plastic mount on the 18-105 lens (which I've since replaced) and ended up buying a Tamron 18-270 with a metal mount while on vacation.
That's why I've got some hesitation buying the D5100. I can just see the same thing happening to it as the D3100. Shoot, maybe I should just jump into that D7000 instead of waiting to see if the next version comes with a swivel display.