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.