The functionality of the middle mouse button in Modeler mirrors that of the stock Houdini. However, holding down the Ctrl key introduces a modification. Specifically, it triggers an automatic adjustment to the handle alignment preference under "Houdini Preferences/Handles/Translate Handle". If the current setting is "Drag in View Plane", pressing Ctrl temporarily switches it to "Map Drag to Axis". Conversely, if the setting is "Map Drag to Axis", pressing Ctrl changes it to "Drag in View Plane" for the duration that the Ctrl key is held down.
Modeler has no built-in Cycle Handle Alignment tool, but the Houdini version can be invoked with the M key. By default M is not assigned in Modeler.
QuickPivot changes the position and orientation of most of transformation handles.
If you want to remap this tool's hotkey do not use hotkey with modifiers.
For example, D is a good hotkey. But Shift+D will not work correctly.