Nikon's 300 2.8 AF-S lenses focus very rapidly. Not sure how you have the AF system set up, but many people find that using more than one AF point helps the Nikon AF system to follow moving subjects better, since there are more data points than just "one" point. I have the older 300/2.8 Mark II, the last model with the aperture ring, and the lightweight magnesium barrel; that lens is a very fast focuser. It was made just before the VR model hit the streets. Right now, 70-200 VR I's are going for $1200 used, so lots of those are hitting the market now that there is a VR-II model.
Most of my nighttime sports have been prep soccer, played under atrociously poor lights, and for that the 200 f/2 has been a good lens. It can be used full-field, and the f/2 aperture gathers double the amount of light as the 300/2.8 AND with the front-mounted FUNC button programmed to switch the camera from FF to the 2.0x FOV crop, the Nikon you have would give you superb lens quality at 200mm, and then also an in-camera equivalent field of view of a 400mm ,yet still with f/2 focusing accuracy--all with just one push of the FUNC button to swich back and forth between FF and High-Speeded Crop mode. A 300mm lens is *tight* when action comes toward your camera position if you are on the sidelines, but it's great if you are farther away. It's too bad Nikon does not make a pro-capable 60-250mm f/2.8 lens or something similar, for sports/action uses.
Baseball is another matter entirely. Depends where you are shooting from, either near 3rd base or near 1st base,and what position your son plays. If he is an outfielder, the longer the better. A friend of mine shoots a LOT of minor league baseball games and uses an 80-400 Sigma,and does well on that as long as the light is good. I like the AF speed of the 300/2.8 on the D2x for baseball, but the focal length is too long to shoot from the dugouts, either the home or visitors, so I end up down by 3rd base with the 300 prime. For daytime Baseball, I normally use my Sigma 100-300 f/4 HSM because it allows me to get more shots of more things from more shooting areas. If you want to focus on one,specific player, like if your son plays 1st base or shortstop or 2nd base, then a longer lens shot from over around the 3rd baseline area would make a lot of sense. If he plays right field though...300mm is not too long. A crop-body Nikon that offers 1.5x AND 2.0x FOV might be a good addition for baseball--it shifts the lenses and their effective focal lengths around, and baseball is normally played in really good,bright lighting conditions compared to nighttime HS football.