MAYBE you might be able to get acceptable images with the 55-250 at a professional game where the rink/court is well lit, but for the kids, who would be playing in not-so-well lit arenas, it won't be enough. It's not the amount of zoom that's the problem, it's the amount of light the lens can provide to the sensor. f/4.0-5.6 is too small. You would have to use a very high ISO to get a good exposure, which increases noise...meaning photos that are soft and/or grainy looking. It also means that the shutter speed would be slower, making for blurry images.
Unfortunately, the type of zoom lenses required for indoor sports are very expensive; they can easily be double or triple your budget.