May a mother and teenage son swim together?

Shalom U'vracha, It is forbidden for men and women to swim in a body of water together, such as a pool or beach. Even in an area where women are dressed modestly, and religious people may frequent on a hike, such as a natural spring, one should not swim mixed because the water may emphasize bodyparts that could draw attention to it in an immodest fashion. However, in a place where only the close family is present (as I understand from your question) there is more room to be lenient about allowing it. In that situation--and with the strictures of modesty in place--a mother and her teenage son would be allowed to swim together.