Does our father have the right to claim a portion of the proceeds from the business that grew through his effort and work with our grandfather, as a right for us (his children), because he did not work for his personal account?

The father does not have the right to claim a portion of his father's wealth as an established right for his children as a result of his work with him. Rather, he himself has the right to claim his due if he was not volunteering his work, and the reference for this is custom. As for the children, they have no relation to their grandfather's wealth, and their father's work with him does not establish a right for them in it as long as their father is alive.