Portraiture usually means a large aperture lens, so you can take advantage of a shallow depth to accentuate the subject. Portraiture of children usually means a longer focal length, so you don't have to be very close to get the shot. There are a number of lenses that will work well for that including Sony's 100/2.8 (~$600), Sigma's 105mm f/2.8 (~$400) and Tamron's 90mm f/2.8 (~$360). All are quite good. You may want to drag a child with you when you return to the store, so you can best see the effects of the focal length and aperture.
For outdoor sports, especially the sports you mentioned, aperture isn't such a big deal, but focal length is. At a minimum, the Sony (Tamron) 55-200/4.0-5.6 (Sony:~$230, Tamron: ~$125 after rebate) is nice, as is the Minolta 70-210/4.0 'Beercan' (~$200 used), but something longer might be better. There is the Sony 70-300 'G' (~$750 on sale) which is the best of it's kind, but if that's a little steep, there are other, more affordablechoices. None of them are very good, but probably the best among them is the Tamron 70-300 Di LD (~$170). The Sigma 70-300 (~$210)is ok, buthas a history of failing when connected to Sony dSLRs. The Sony 75-300 (~$230) is inferior to the other two and more expensive.