My summer pool experiences circled around many a motel pool, as we traveled as a family, while my dad played softball. We also spent a fair amount of time at our grandma's house, in Saratoga - with aunts that would use a bandana for our swimming suit top - and take us to the "hobo pools," that were hot springs. So we had our fair share of chlorinated, as well as fresh, rotten egg smelling pools.
Would I trade those experiences for the beach? Probably not. Aside from spending time with fun aunts and children from other towns, we did have a few "country club" experiences in which the waiter (and yes, he came out to the pool with our chocolate mousse) dropped his glasses in the pool (one of us had to fetch them for him) and in turn, he almost fell in, too!
While you may not get the country club experience, there are a few options for pools in Sheridan, and you'll get a chance to relax, and if there are littles involved, they'll get nice and worn out!