Place the mixture in a cup of the ice cream maker and process as recommended in the manual. When the sorbet is almost ready (5-7 minutes before the end), add the rum. The sorbet will remain soupy, and could use it at once or place in the fridge for a while.
To make the dressing, place all the ingredients, except the rum, in a cup of your blender and process until smooth. Strain and discard the seeds.