Is it permissible for a woman to lighten her face covering around her eyes so she can see the path, especially after falling multiple times, and is she obliged to obey her husband who refuses this and says: "There is no harm if you fall for the sake of obeying me"?

If a woman is able to cover her eyes with a light veil that allows her to see, she should do so in obedience to her Lord and her husband. However, if not removing the veil leads to her falling, then there is no harm in uncovering her eyes as much as needed to see the path, and the husband should understand that.