You can use [IShow] to show a palette at the cursor position. If the palette is in the right or left tray then it will be opened there instead (or if it’s already open, nothing will happen).
This will cycle through three palettes as you press the hotkey. You could extend it to more palettes easily enough but make sure to use the loop otherwise it will just show the last palette (having quickly run through them all).
[IButton,???,“Use hotkey to cycle palettes at cursor”,
A note about hotkeys with macro or plugin buttons: if your hotkey includes a modifier key such as SHIFT you need to repress it for repeat presses - it won’t work if you hold it down and just press the other key. For example, if your hotkey is SHIFT+Q you’ll need to press both keys each time.