How did the women turn in prayer at the Mosque of Qiblatayn after the change of the Qiblah, and is there a sound, established story about how the change occurred?

The story of the Qibla's change from Bayt al-Maqdis to al-Masjid al-Haram is affirmed in the Quran and Sunnah. The Prophet (peace be upon him) prayed towards Bayt al-Maqdis for sixteen or seventeen months, then verses were revealed commanding him to turn towards al-Masjid al-Haram. The Prophetic traditions illustrate how the Companions turned during prayer after learning of the change, with the Imam and congregants making a semi-circular turn. As for visiting the seven mosques and places in Medina with the intention of worship and gaining reward, there is no basis for this.