All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Slaughtering a sacrifice is not due on the woman who has been prevented by her injury from coming in and standing at Muzdalifah, especially given that it was impossible for her to be transported by car too. The juristic scholars state that nothing is due on the one who misses standing at Muzdalifah due to a legal excuse.
Ash-Sharh Al-Kabeer on Mukhtasar Khaleel, which is a book on the Maaliki Fiqh, says:
"One is recommended to spend the night in it (Muzdalifah). To stay in it is an obligation, even as short as is equal to unloading their luggage, even if they do not actually unload it. Leaving this obligation requires offering a sacrifice … if one does not stay in it even as short as is equal to unloading the luggage till dawn rises, then a sacrifice becomes due on him unless there is a legal excuse."
Commenting on that, Ad-Dusooqi said, “That is, except if there is a legal excuse due to which he has not stayed in it, in which case nothing is due on him.”
Allaah Knows best.