I don't get it....
Swinging is another term for having sex with someone else's partner. However, in this case, it is about going to the playground to swing on the swings with the kids.
From Wikipedia:
Swinging, sometimes referred to as the swinging lifestyle, is a non-monogamoussubculture, treated much like any other social activity, that can be experienced as a couple. [1] The phenomenon of swinging (or at least its wider discussion and practice) may be seen as part of the sexual revolution of recent decades, which occurred after the upsurge in sexual activity made possible by the prevalence of safer sex practices during the same period. Swinging was once called wife swapping in the past, but this term has been criticized as androcentric and inaccurately describing the full range of sexual activities in which swingers currently may take part in today's society. It reflects the origins of swinging of actually swapping wives.