WHAT?! the 28-200mm versus these excellent lenses?! these lenses are 567384563945 centillion times better than the extremly-soft-at-all-focal-lengths 28-200mm. there is quite a difference.
the f/2.8l series is different, and may be too much for you. they are 3 times heavier, and i think it might be overkill for just children, family stuff, but if you want to spend the $1.6K, it is worth it. you may want to rent it, because while 3lbs might sound light to you, if you spend 3 hours with it photographing running children and taking pictures of candles on a cake with a smiling kid in the background, it will be HEAVY. the newer II IS version, which is even more overkill to you maybe, is sharp at all apertures, including f/2.8, (which the original, was soft at a little).
ok if you don't want to read an essay, READ THIS PART:
i recommend the 70-200mm f/4l is usm, because its light (compared to its bigger brother and sister, the f/2.8l series), you do outdoor stuff (which you really don't need f/2.8 for), it has fast AF performance (better than the DC motor of the 70-300mm), and its very sharp. if you have no budget and lost your mind slightly, then spend it all on the f/2.8L IS USM II. but budget wise, and commonsense wise, the 70-200mm f/4l is usm is for you. plus, its weather sealed, unlike the non IS counterparts, so you can take some good pictures on a rainy little league baseball game.
the 85mm is a different story, and if you must, then buy the 85mm f/1.8, because its boatloads cheaper, lighter, and sharper