Is it permissible to take the difference in wages for the extra hours worked from the employer who violated the agreement by employing the worker in a field other than his specialization and for a longer number of hours, and if the employer refuses, is it permissible to secretly take this difference from his money that is under the worker's hand?

The one who contracted with you for teaching must fulfill the contract regarding the type of job, its time, and working days, unless the contract stipulates the permissibility of change. As for you, as long as you accepted the last job after the change, you are obligated to continue with it until the end of the contract. It is not permissible for you to take any money secretly, for that is treachery and theft.