Good interface design always allows alternative way to do things.
Keyboard commands are always faster than mouse/palette/menu choice commands.
The pet palette is an additional way to do things.
If you don't like it, fine. Perhaps this means being able to control when it appears, not terminate it.
I would be for a pet palette along the lines of the contextual menu structure in Maya where an array of choices much like a decision tree appear surrounding the mouse when summoned. The cursor should be in the middle of a number of choices that hover, partly transparent, over the work.