Not really a "private club" if it has an "open" membership. A real priviate club, invites people to join and does not have an "open" membership. Open membership means anyone that can afford the membership fee is free to join. In other words it is a PUBLIC club with a membership fee. They are screwed.
From what I've read, this was a special arrangement with the day care center, not a set of memberships. They don't appear to have denied anyone a membership, rather reneged on a contract. It's still not good; the management messed up in a big way by not anticipating the problems of this huge influx of kids from outside the neighborhood, regardless of ethnicity. There are municipal pools sprinkled throughout our area. This would have been a better arrangement for the day care center, since they are typically larger and better able to manage these numbers of incoming swimmers.
I bet their “open” membership has a right of refusal.
The way I see it at this point, at most you have a contract dispute, assuming the groups had contracts with the club and the club did not have escape clauses built into their contracts.
Its all a matter of are they a club or a business, if they are a club they are free to do whatever they want. If they are a business they would be screwed.