“Could you clarify the difference between Dati Leumi and Modern Orthodox? For example, you mention that he forbids women from wearing pants. Is this in contrast to Rabbi Shachter, who is modern orthodox?”
Most Modern Orthodox Jews are Dati Leumi, but not all Dati Leumi are Modern Orthodox. Religious Zionists can range anywhere from very Modern to very Chareidi.
Rav Schachter doesn’t permit women to wear pants. He says that if Beis Din were around nowadays, the would give a woman who wears pants malkus.