I can try to find one, but it should be a simple kal v’chomer, since other parts, even for married women, are still more chamur than hair – it is muttar meikar hadin to have hair uncovered in the home, but not other, normally covered, parts.
I don’t know how women conduct themselves at the pool, but even if you’re correct, and even if it’s not a mistake, it could simply be because there’s no need for the hair to be uncovered; in fact bathing caps are usually required.