If this is a pool party, I do not think it is rude at all to request that it be outside and to bring lawn chairs. Most people don't have enough outdoor chairs for a big party, and that request is pretty typical in my neck of the woods. I know some people say that hosts should not be upset if people end up inside when the party is outside, but I see no big deal with keeping everyone outdoors unless they need a restroom. If the weather cooperates, there is no real reason (other than a health need) to be indoors, and in that case I might exuse myself because sitting in the house away from others isn't the point of the party (barring emergencies, of course).
The pool thing is a little odd, but I can totally see the point. My inlaws have a pool and I've seen how quickly things can get out of hand if there are too many kids. Since this is a team party, I can see why the host would want to make sure those kids enjoy the pool.
In this case, I would have just invited the softball team. The host is going to have some upset siblings on his or her hands.