Is it permissible to make the school mosque into a place in which children play at times other than the prayer times?
Question

The masjid in our community also consists of a school for children where they are taught religious and secular education. The classes for children are held in separate rooms but the masjid and school are built within one building. Due to the limited space in the building, the masjid area is used as a playing ground for children at times other than Salah. This also prevents people from praying in the masjid at other times due to children playing there. Is it permissible to allow the children to play in the masjid regularly and would this be considered a sin ?
Praise be to Allah.The mosques are the houses of Allah and are only built to remember and worship Him. It is prescribed to purify them and clean them of anything that may spoil them. Allah, may He be exalted, says (interpretation of the meaning):
“In houses (mosques), which Allah has ordered to be raised (to be cleaned, and to be honoured), in them His Name is glorified in the mornings and in the afternoons or the evenings,
Men whom neither trade nor sale diverts them from the Remembrance of Allah (with heart and tongue), nor from performing AsSalat (Iqamat-as-Salat), nor from giving the Zakat. They fear a Day when hearts and eyes will be overturned (from the horror of the torment of the Day of Resurrection)” [an-Noor 24:35-37]. 
Please see also the answer to question no. 93809 
This does not mean that it is not permissible to gather there for the purpose of some leisure activities such as talking about permissible things, eating, drinking, and relaxing, especially on the Eids, so long as that does not become a regular habit in the mosques that diverts from the purpose for which they were built of remembering Allah, establishing prayer, reciting Quran and holding classes for gaining knowledge. 
Please see the answer to question no. 141553 
With regard to making the mosques, outside of the times of the prescribed prayers, a place where children can play in an organised fashion and on a regular basis, that is not permissible; rather it is obviously wrong, because of what it involves of imposing time restrictions on worshippers at that time, and making the mosque unavailable for the purpose for which it was built, and because it also will lead to the mosques not being respected and being exposed to the risk of contamination with dirt and impurities on some occasions, and it will expose some items in the mosque to damage, and expose the Mushafs and Islamic books to harm at the hands of children, because young children usually, if given free rein, do not refrain from spoiling things and damaging them, and doing whatever they please the place in which they play. 
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 
The mosque should be protected from things that will damage it and disturb the people worshipping in it, even children and raising their voices and making dirty the carpets and so on, especially if it is the time of prayer, because that is one of the gravest of ills.
End quote from Majmoo‘ al-Fatawa (22/204) 
See also the answer to question no. 121550 for information on the reality of secularism and the reality of their evil views. 
And Allah knows best.