Sam2,
I am not arguing on R’Moshe. I am explaining R’Moshe.
You and your sister are talking about different things. The requirement to walk around with a body part covered is different from the prohibition of davening in front of erva. Don’t conflate the two and the contradiction disappears.
A married woman is required to cover her hair m’d’oraisa. Not davening in front of uncovered hair is a d’rabbanan, which, according to R’Moshe, does not apply if women habitually violate the halacha and don’t cover their hair.
A women is not allowed to uncover her arms in public because of Daas Yehudis. Not davening in front of uncovered arms is d’rabbanan which applies, according to R’Moshe, even if women habitually don’t cover their arms.