Should Muslim women be allowed to pray in the mosque?

Allah (SWT) is not merciful to those who are not merciful to others.
 "Do not prevent your women from attending the mosque if they seek your permission to do so."Ibid., 4/161

  "If your womenfolk seek your permission to go to the mosque, then let them do so." Sahih Muslim, 4/161, kitab al-salah, bab khuruj al-nisa' ila'l-masajid.

Islam has excused women from the obligation to attend the  jama`ah prayer in the mosque, but at the same time, they are permitted to go out of the house to attend jama`ah  on condition that they dress up well enough not to cause any temptation. Indeed, the first Muslim women did go out and pray in the mosque behind the Prophet (PBUH). `A'ishah (May Allah be pleased with her) said:

Allah 's Apostle said, "Treat women nicely, for a women is created from a rib, and the most curved portion of the rib is its upper portion, so, if you should try to straighten it, it will break, but if you leave it as it is, it will remain crooked. So treat women nicely."

Islam has excused women from the obligation to attend the  jama`ah prayer in the mosque, but at the same time, they are permitted to go out of the house to attend jama`ah  on condition that they dress up well enough not to cause any temptation. Indeed, the first Muslim women did go out and pray in the mosque behind the Prophet (PBUH). `A'ishah (May Allah be pleased with her) said:

The Prophet (PBUH) used to shorten his prayer if he heard a child crying, because he understood the concern the child's mother would be feeling. In a hadith whose authenticity is agreed upon he (PBUH) said: "I begin the prayer, intending to make it lengthy, but then I hear a child crying, so I shorten my prayer because I know the stress facing the mother because of his crying."9Allah (SWT) showed great mercy to women by sparing them the obligation to offer the five compulsory prayers in congregation in the mosque. If He had made this obligatory, it would have placed an intolerable burden on women, and they would not have been able to fulfil it, just as we see many men failing to pray regularly in the mosque and finding themselves with no other choice but to pray wherever they are, in the workplace or in the home. The woman's heavy burden of household chores and attending to the needs of her husband and children do not permit her to leave the house five times a day; it would be impossible for her to do so. Thus the wisdom behind the limiting of compulsory attendance at the mosque to men only becomes quite clear. Her prayer at home is described as being better for her than her prayer in the mosque, but Allah (SWT) gives her the freedom of choice: she may pray at home if she wishes, or she may go out to pray in the mosque. If she asks her husband for permission to go out to the mosque, he is not allowed to stop her, as the Prophet (PBUH) stated in a number of hadith, for example: "Do not stop your women from going to the mosque, although their houses are better for them."

The mosque was, and still is, the centre of light and guidance for Muslim men and women; in its pure environment acts of worship are performed and from its minbar messages of truth and guidance are transmitted. From the dawn of Islam, the Muslim woman has had her role to play in the mosque.

There are many sahih reports, which confirm the woman's presence and role in the mosque. They describe how women attended salat al-jumu`ah, the eclipse prayer, and the Eid prayers, responding to the call of the muezzin to join the prayer.

  During that golden era, the time of the Prophet (PBUH), the Muslim woman knew about her religion and was keen to understand the events and affairs that concerned the Muslims in this world and the next. When she heard the call to prayer, she would rush to the mosque to hear the words of the Prophet (PBUH) from the minbar, guiding and teaching the people. Fatimah bint Qays, one of the earliest migrant women (muhajirat), said:"The people were called to prayer, so I rushed with the others to the mosque, and prayed with the Messenger of Allah (PBUH). I was in the first row of women, which was just behind the last row of men."19
 
 Muslim women attended the mosque on various occasions and that this attendance was an approved custom at the time of the Prophet (PBUH).
 The Prophet (PBUH) appreciated the circumstances of the women who attended the congregational prayers, so he used to be kind to them and would shorten the prayer if he heard a child crying, so that the mother would not become distressed

Bukhari and Muslim also report a hadith concerning how women should draw the imam's attention to something during the prayer by clapping. Sahl ibn Sa'd al-Sa'idi said: "The Messenger of Allah (PBUH) said, `Why do I see you clapping so much? Whoever notices any error in my prayer should say "Subhan Allah ," for by doing so he will alert me to the error. Clapping is only for women.'"\

Prophet (PBUH) said:"Do not stop your women from going to the mosque, although their houses are better for them."

It is permissible for Muslim women to attend the gatherings of the Muslims in the mosque, and there is much to be gained from them doing so, but certain conditions apply to this permission, the most important of which is that the woman who goes to the mosque should not wear perfume or make-up. Zaynab al-Thaqafiyyah reported that the Messenger of Allah (PBUH) said:"If any of you (women) wishes to attend `isha' prayer, she should not wear perfume that night."

You go to Saudi Arabia… women are allowed in the Mosque, you go to London… women are allowed in the Mosque, you go to America, Malaysia and more women are allowed in the Mosque.  You go to the Haram-Sharif in Mecca, in Masjid-e-Nabwi, they are allowed.

So if separation and dignity of women is maintained in mosque than there is no binding of praying in mosque.