All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The father must abide by the conditions and terms of the employer unless he authorizes him to be accompanied by his family, because of the general saying of the Prophet : “The Muslims should abide by their conditions.” [Abu Daawood]
You and your mother must abide by that even if your father invites you to travel, as a way of you abiding by the condition (set by the employer) and which does not contravene the Sharee’ah of Allah and which fulfills the interest of the employer. Any condition which fulfills the aforementioned matters which are Islamically advocated must be abided by.
Calling such rules as man-made rules and the like, does not harm.
Allah knows best.