We understand from this question that was submitted to the website that what is meant by the ‘iddah in this question is the ‘iddah following divorce (talaaq). Based on that, it should be pointed out to the sister who is asking this question that the ‘iddah following divorce (talaaq) must be one of two things:
1. Either ‘iddah following a revocable divorce
2. Or ‘iddah following an irrevocable divorce.
In the first case: she is observing ‘iddah following a revocable divorce. She may go out to the mosque or to Qur’an classes on condition that her husband give her permission, because the woman who is revocably divorced is still a wife, with the same rights and duties as other wives.
It was narrated from Ibn ‘Umar that he used to say: If a man has divorced his wife once or twice, she should not go out of her house except with his permission.
Narrated by Ibn Abi Shaybah in his Musannaf, 4/142
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The more correct view is that if the divorced woman’s divorce is revocable, then she 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 talks and so on. She is not like the one whose husband has died. With regard to the verse (interpretation of the meaning): “and turn them not out of their (husbands’) homes, nor shall they (themselves) leave” [at-Talaaq 65:1], what is meant by turning them out is leaving, i.e., she should not leave the house and go out and live somewhere else.
End quote from Fataawa Noor ‘ala ad-Darb.
An-Nawawi (may Allah have mercy on him) said: If she is revocably divorced, then she is still a wife; he still has to take care of her maintenance, and she should not go out except with his permission.
End quote from Rawdat at-Taalibeen, 8/416
In the second case: she is permanently divorced, whether she is completely divorced and cannot go back to her husband unless she marries another man in a genuine marriage, then he divorces her or dies (baynoonah kubra), such as when the number of talaaqs has been used up, or she is completely divorced but may go back to him with a new marriage contract (baynoonah sughra), such as when she has asked him for khula‘ in return for compensation, or the marriage has been annulled because of some defect. In this case it is permissible for her to go out, even if it is without permission, because she is no longer a wife.
It was narrated from Ibn ‘Umar (may Allah be pleased with him) that he used to say: If a woman has been divorced, then she may come to the mosque and it is her right to do so, but she should not stay overnight anywhere except in her house, until her ‘iddah has ended.
It says in Mughni al-Muhtaaj, 5/174: The woman in ‘iddah who is completely divorced by means of khula‘ or three talaaqs is not entitled to of maintenance or clothing at all, because she is no longer a wife. Her case is similar to that of the one whose husband has died. End quote.
In Haashiyat al-Bayjurmi, 4/90 it says: With regard to the one who is entitled to maintenance, such as one who is divorced but still in her ‘iddah, or one who is completely divorced but pregnant, they should not go out for that except with the permission of the husband, like any other wife, because he is still obliged to provide them with maintenance. However, the one who is pregnant may go out for purposes other than seeking maintenance, as mentioned by as-Subki and others. End quote.
To sum up:
If a woman is in ‘iddah following a revocable divorce, it is not permissible for her to go out except with her husband’s permission. But if she is in ‘iddah following an irrevocable divorce, then she may go out if she needs to, even if that is without permission, because she is no longer a wife.
And Allah knows best.