What is the authenticity of the saying that a divorced woman should not leave her home until the waiting period (iddah) expires, and that reconciliation (raj'ah) is not considered a divorce unless the husband does not take back his wife during the waiting period, along with a request for evidence from the Quran, Sunnah, and the guidance of the Rightly Guided Caliphs?

It is not permissible for a wife to leave her home during the waiting period ('iddah (definition)), nor is it permissible for her husband to expel her, as Allah Almighty says: ﴿Do not expel them from their homes, nor should they leave, unless they commit a flagrant indecency.﴾ As for the statement that a husband’s return to his wife during her 'iddah does not count as a divorce, this is a false statement. The people of Jahiliyyah (pre-Islamic ignorance) used to do this to harm women, then that was abrogated by Allah Almighty’s saying: ﴿Divorce is twice. Then, either keep [her] in kindness or release [her] with good treatment.﴾ Al-Qurtubi explained in his Tafsir (definition) that this verse abrogated what the people of Jahiliyyah practiced regarding not limiting the number of divorces.