Drupal - Quick Uninstall/Reinstall of a Custom Module
Solution 1. Devel + Drush:
You can use devel drush command for module re-installation with all the module dependencies:
drush devel-reinstall modulename
There is also alias for this command
drush dre modulename
Solution 2. Drush:
This is something that I would typically use drush for
drush pm-disable mymodule
drush pm-uninstall mymodule
drush pm-enable mymodule
You could also use it to define your own custom commands to combine these into a single command.
If you don't have shell access the Devel module provides such functionality. Install it and visit mysite.com/devel/reinstall.