We find ourselves confronted with the age old problem of not enough glass and how to make the best of a bad job. Using the zoom lens, which at the price is the one I would have recommended anyway, try taking some shots at ISO1600 and 1250, but using aperture mode to keep the lens as wide open as possible. See what shutter speed it is giving you. If it is less than 1/60th then any action shot will be naturally blurred, but baseball is a sport with it's quiet moments where you can still take good shots especially in well lit areas. Incidentally at 300mm you'll be restricted to F5.6 anyway. The danse recital is another thing entirely, and because it is normally not that well lit unless you can use flash and have at least the SB600 then I am afraid you are not going to be in a very good position here.
All I can suggest is that you do some trial and error indoors with the family for the dance recitial and approximate the light for a trial and error session for the baseball. At the end of it all I am afraid that this subject has been oft discussed here, and there is no substitute for big glass. I have recently bought the 200/400 F4 Nikkor for just this reason, although it nearly bankrupted me. But for professional motor racing photography, and golf too, good glass is all important to get the car/player in full focus with the background blurred. Getting a quart out of a pint pot has always been difficult! best of luck.