I would go with a D80 and the Nikon 18-55mm. Get a new body and a good lens. Used bodies are a bit of a gamble to me and the peace of mind that you have a new body with warranty is better than a used one that has nothing. Getting a cheaper lens with more focal length flexibility will be nice at first but you will soon find that lens has some drawbacks to image quality.
Take your time with lens acquisition and keep on the lookout for deals that come by now and again. I did with a Nikon 28mm 2.8 for $70 which out does the Tamron 28-75mm 2.8 that I have. I have the Nikon 50mm 1.8 and got it for $60. All said and done if I had waited before getting the Tamron I would have saved $245.
Now that you know what you want in a camera system. Don't make lens purchases just for the sake of having a lenses to cover all focal lengths. Be patient and get the best glass at the best price.
Oh by the way, I think the 18-55mm VR is a bit of an overkill on a lens. For me VR at that focal length is not truly a necessity. You will find that 18-55mm (non VR)is quite an acceptable lens but not a low light performer like the 50mm 1.8. The 50mm 1.8 is not a great lens for cramped quarters indoors though.
I have the Tamron 17-50mm 2.8 and like it very much. One third the cost of the Nikon equivalent.
If I were to start over like you I would go with a new D80 body and look at Abes of Maine for that.
The lens is a bit of a stretch based on what you primarily shoot so the 50mm 1.8 for your kids indoors would most likely not be a good choice.
I would go back to the Nikon 18-70mm or get the Tamron 17-50mm 2.8