Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah preserve him) who replied that it is not permissible to pray outside the mosque except in cases of necessity, and this is not a case of necessity. The women who have children with them (who disturb others) should be told not to come at all, because they are causing annoyance to others, or else they have to pray outside the mosque without. So this tent should not be put up for them outside the mosque. And Allaah knows best.