Does the son's unwillingness to work with his father in his private schools, and his preference to work in his engineering field for companies, constitute disobedience?

You are not obligated to work with your father in his field, and leaving work with him is not considered an act of disobedience (uquq). However, you should be gentle with him, apologize courteously, and convince him of your point of view. If you do work with him, intending it as an act of piety for his sake and seeking his pleasure, that would be better for you.