Its possible that Mamila can arrange access to the David Citadel Pool, as they are sister properties across the street from each other.

Main issue with the Jerusalem Hotels (not sure about KD) is that they sell access to outsiders on a daily or monthly basis. When I lived in Jerusalem we had a membership at the Inbal and brought the kids regularly.

If you swim in the mornings or early afternoon during school season then the KD or DC are usually quiet. Otherwise, expect a crowd.