Is it permissible to divide work, so that each employee works 4 hours instead of 8, even though the hospital director does not allow it?

You must adhere to the binding agreement of working 8 hours daily, as long as the direct manager does not permit less than that, due to the Almighty's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (PBUH) saying: "Muslims are bound by their conditions." Showing courtesy to the duty manager does not permit dereliction of duty.