She is observing ‘iddah in her family’s house and want to go out to Qur’aan study circles

Praise be to Allah.

Firstly: 

If a husband divorces his wife with a revocable talaaq, the woman is obliged to observe ‘iddah in her husband's house, and if she goes out without a valid reason she is sinning and she has to go back until her ‘iddah ends, because Allah, may He be exalted, says (interpretation of the meaning):

“And turn them not out of their (husband’s) homes nor shall they (themselves) leave, except in case they are guilty of some open illegal sexual intercourse”

[al-Talaaq 65:1].

And she should stay there so long as she does not fear that some harm may befall her. See also the answer to question no. 122703. 

Secondly: 

It is permissible for a woman who has been divorced with a revocable talaaq to go out to the mosque and to Qur’aan study circles, on condition that her husband gives her permission, because the woman who has been divorced with a revocable talaaq is still a wife, with the same rights and duties as any other wife. 

It was narrated from Ibn ‘Umar (may Allah be pleased with him) that he used to say: If a man has divorced his wife (talaaq) once or twice, she should not go out of her house except with his permission. Narrated by Ibn Abi Shaybah in al-Musannaf (4/142). 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The correct view is that the divorced woman, if it is a revocable divorce, is like a wife who has not been divorced, i.e., she may go out to visit her neighbours or relatives, or to go to the mosque to listen to exhortation and the like. She is not like the one whose husband has died. With regard to the words, “And turn them not out of their (husband’s) homes”, what is meant by turning them out is leaving, i.e., they should not leave the house and go and live in another house.

End quote from Fataawa Noor ‘ala al-Darb. 

Al-Nawawi (may Allah have mercy on him) said: If it is a revocable divorce, then she is still his wife; he has to take care of her and provide for her, and she does not have the right to go out except with his permission.

End quote from Rawdah al-Taalibeen, 8/416. 

To sum up the answer: she has to go back to her husband’s house until her ‘iddah ends, and she has the right to go out during this period, if her husband gives her permission. 

And Allah knows best.