The Eida HaChareidis1 paskened (and R' Wosner agreed) in accordance with the Mishna Berura2, who requires women to go in public places only when wearing redid (a head-covering wrapping the entire body like men wear a talis3) concealing the triangular space between head and shoulders, and the split between arms and torso. This applies even today.4
According to R' Moshe Feinstein5 a woman may select any posek she wants, even if her husband is a posek. Indeed, no wife of any of these poskim followed their husband's psak. It is also the prevalent custom not to follow this, although some do.6
Which poskim would they be following?7
1. Written kol koreh by R' Weiss with R' Fisher, R' Rabinowitz, R' Halberstam, R' Bernsdorfer, and R' Ulman.
2. Biur Halacha on Siman 75: Veda shekol ze (...) le kula alma (...) overes al das yehudis...
3. Rambam Hilchos Ishus Perek 13 & 24, Shulchan Oruch Even HaEzer Siman 73.
4. Diyuk in Rambam ibid. shenohagu bnos yisroel and not shenohagin i.e. it doesn't change according to current custom.
5. Written by R' Leib Tropper in the name of R' Feinstein's son.
6. At least in Bet Shemesh, Jerusalem, Kiryas Joel, London, Monsey, and Montreal. E.g. one of the two Shomer Emunim Rebbetzins, and R' Shlomo Brevda's daughter-in-law.
7. It would seem that they would be either later than the Mishna Berura, or that he did not know (or consider) them.