I know about the light ability of a f/1.8 prime but I think for a general running around with kids during the day, the f/3.5-4.5 should be enough. I am currently exploring the following lenses:
24-85mm f/3.5-4.5 AF-S G
28-70mm f/3.5-4.5 AF-D
20-105mm f/3.5-4.5 AF-D
Still leaning towards the 28-70 due to the price and size (I will get more lenses down the road so that wouldn't be my only lens). Next one would most likely be the 35mm f/1.8mm lens (I grew up with film and 50mm lenses).