Is there a nail in there already? If it’s rocking in place, the glue might have failed already and it’s only held in place by a previous crappy fix. I have two that were like that. I removed the nails and glued it back after adding a thin piece of wood to both sides and taking shavings off until I had a tight fit.
Removing the nail or the handle can be tricky. I honestly don’t remember how I did it.