It is nowhere expressly forbidden in the Quran to kill women and children, or anyone else for that matter, therefore it must be permitted to kill women and children if a Muslim believer does it with the good intention of serving Islam and the prophet. Anything that increases the power of Islam in the world is good by definition. This is the supreme end of all Islamic activity and the Ummah itself.
If believers are also caught up in the carnage that is just unintentional collateral damage which Allah will dutifully forgive but it should be avoided if possible. This is why Jihadists try to filter out Muslims during their killing sprees.
If a believer claims that he killed women and children with good intention no one can dispute this, not even Allah and his prophet. Therefore this action is always good if it is done with good intention. This is Islamic ethics 1 on 1. The end always justifies the means. If someone believes that whatever he does is for the benefit of Islam then it is permissible. No one can say otherwise. Allah is not bothered about a bit of infidel blood. He is in it for the long haul. The Dzhokhar and Tamerlan Tsarnaev brothers who did the Boston Marathon bombing are a good example of this:
|Boston Marathon bombing|
The area of the first blast a few minutes after the explosion
|Location||Bombing: 671–673 and 755 Boylston Street, Boston, Massachusetts
Shooting: Corner of Vassar Street and Main Street inCambridge, Massachusetts
Firefight and manhunt:Watertown, Massachusetts
|Date||Bombing: April 15, 2013,2:49 pm EDT
Shooting: April 18, 2013,10:48 pm EDT
Firefight and manhunt:April 19, 2013, 12:30 am –8:42 pm EDT