For the D3100, which doesn't have an in-built autofocus motor, you'll need an AF-S lens. That rules out the f/1.8 "D" lenses (35, 50 and 85mm), leaving the f/1.4 lenses and the newer f/1.8 "G" lenses.
Outdoors you don't need f/1.4, and those are expensive lenses.
35mm is often a good focal length indoors where space is limited, but outdoors 50mm and 85mm are probably better choices. If you want out of focus backgrounds, a longer focal length helps. The 85mm produces gorgeous images - nice bokeh and a good length for portraits, as long as you can keep the kids in the frame!
I find the 35mm and 50mm are more versatile overall than the 85mm. I take 10x more shots with my 50mm than my 85mm, but on the occasions when the 85mm is used, it's stellar. You won't be disappointed with the 85mm, but you may get more use out of the 50mm. Also depends on what other lenses you have.