As an employee in the State of Qatar you need and exit permit to leave the country. Yes, no freedom. Your company must approve for you to leave the country even if it's your days off. Two options. Single exit permit or Multiple Exit Permit.
Multiple Exit Permit can be obtain with an approval from the company and you have to pay QAR 500 (USD 136.98)
As for your family, they are free to enter and exit the country anytime they please after RP (residence permit) has been obtain.
Welcome to the Middle East. It's another world.
