The Solar System has many potentially habitable ocean worlds, some of which contain significantly more water than Earth. A number of these oceans are hidden by an icy crust, lack significant land barriers, and are heated from below by the mantle; thus, their dynamics are quite different from Earth. While observations are limited, recent studies have used numerical models to define these planets by different regimes describing the nature of their dynamics and potential for habitability. The effects of convection (thermally-driven movement) and planetary rotation on the movement of heat and materials between the mantle, ocean, and ice on these kinds of planets are explored using a range of rotation and mantle heating patterns. While dynamics due to rotation are stable, it is found that ice-ocean heat exchange is sensitive to the locations of mantle heating. This implies that different mantle heating patterns can affect ice thickness and geologic features that are detectable at the surface, which will allow us to make inferences about ocean dynamics from images of distant planets covered in ice.