MYSQL query to find records between two date range

I am working in a web application using PHP and MySQL.

I have two tables

1. 
   

   Employee
   

   
   

   | employee_id | sup_id | email_id | Password |

   
   


2. 
   

   Coaching
   

   
   

   | coaching_id | emp_id | coaching_start_date | coaching-end_date |

   
   

I want a query to find out the employees who are not enrolled for any coaching program between a specified date range such as Start Date "2015-01-22" and End Date "2015-03-12".

Now I am using query like this,

SELECT employee_id FROM employee WHERE sup_id = 3 AND employee_id NOT IN (SELECT emp_id FROM (coaching) WHERE (start_date NOT BETWEEN "2014-12-26" AND "2015-01-30") AND (end_date NOT BETWEEN "2014-12-26" AND "2015-01-30"))

Where is the issue in my query

Thanks