SoccerMom, Both of these are good cameras, I would recommend the D5000 over the D3000 from what I have read.
As for the blur in the low light pictures, this is a common thing. You will have better chances with a DSLR like the ones mentioned, but there are some draw backs. You will spend about $1300 for a kit setup with the D5000. This gives you a camera, 18-55mm lens that will cover scenic photos and close up stuff, and a 70-300mm lens for zoom. The 70-300 would be needed for sports so you could reach out and get those type shots. (kinda equal to 20X zoom on Point and shoot cameras) The other issue will be a $500 70-300mm lens will behave similar to what you see with your camera now, because it will not gather a lot of light in evening or low light shooting. If you know how to use a SLR or DSLR on manual modes you can pull it off, but in auto you may still have some problems. If you plan on using Auto mode, Sports mode, and those type settings, you may just want to look at getting a better point and shoot. You can get a good point and shoot, with 20X zoom, that still will do the continuous shooting, and have manual modes if you get in to them for a fraction of the cost. Probably around $400.
You may also want to look at a thread I wrote up a while back, it is a sticky in the photography forums thread. It will help explain a few more things.
http://forums.somd.com/photography/143965-what-lens-camera-buy-how.html
I hope this helps