Is it permissible for me to undertake programming work for a client on my own account outside official working hours, with the help of another programmer for a sum of money that I will share with him, after the company refused to do this work?

An employer is not permitted to violate the terms of a contract concerning working hours or wages, and you are not obligated to perform work that was not agreed upon. This is based on Allah Almighty’s saying: "O you who have believed, fulfill [your] contracts," and the Prophet Muhammad's (peace be upon him) saying: "Muslims are bound by their conditions." As for your programming work outside of working hours, there is no harm in it. Similarly, hiring someone else to do the work for you for a lower wage to profit from the difference is permissible, as long as the employer did not explicitly or implicitly stipulate that you must perform the work yourself.