The reason why Helen created the club was not to take away their vacation :)
Not the club per se. They're being forced to go to school during the summer, hence losing their summer vacation time. Or at least a large part of it. Thankfully, The Club is taking up the lion's share of that "lost" vacation, and as the game plot says, Helen trying to have it involve as little actual schoolwork as possible -- but hinted there will be at least some.
By the way, I have a simple answer for what to have the club do (not defined in the game thus far; Our Hero has just returned Helen's keys): charter the school's Fan Film club, and make a movie (Yui's request) about a Final Fantasy X (Sophie's cosplay) blitzball team (Liz's sports)....PROBLEM SOLVED!