I get an exception when re-installing a module
What you have done in the first step is disabling the module, not uninstalling it. To uninstall it, you need to click on the "Uninstall" tab, select that module, and then click on the "Uninstall" button.

The exception raised from DatabaseSchema::createTable() is because it contains the following code. 

  if ($this-&gt;tableExists($name)) {
    throw new DatabaseSchemaObjectExistsException(t('Table %name already exists.', array('%name' =&gt; $name)));
  }


The code in DatabaseSchema::tableExists() is then the following one.

  $condition = $this-&gt;buildTableNameCondition($table);
  $condition-&gt;compile($this-&gt;connection, $this);
  return (bool) $this-&gt;connection-&gt;query("SELECT 1 FROM information_schema.tables WHERE " . (string) $condition, $condition-&gt;arguments())-&gt;fetchField();


You could also manually remove the database table, but if the information about that table is still contained in information_schema.tables, DatabaseSchema::createTable() will raise an exception.