Is it permissible/advisable for my 16year old daughter to sleep over at her non muslim friends house (there will be no males present, only her friend and her friends mother)
Praise be to Allah.
It is not permissible for the Muslim to take a non-Muslim as a close friend, because Allah, may He be exalted, says (interpretation of the meaning):
O you who believe! Take not the Jews and the Christians as Auliya (friends, protectors, helpers, etc.), they are but Auliya to one another. And if any amongst you takes them as Auliya, then surely he is one of them. Verily, Allah guides not those people who are the Zalimoon (polytheists and wrongdoers and unjust)
O you who believe! Take not as (your) Bitanah (advisors, consultants, protectors, helpers, friends, etc.) those outside your religion (pagans, Jews, Christians, and hypocrites) since they will not fail to do their best to corrupt you. They desire to harm you severely. Hatred has already appeared from their mouths, but what their hearts conceal is far worse. Indeed We have made plain to you the Ayat (proofs, evidences, verses) if you understand
[Aal Imraan 3:118].
And there are other verses that forbid loving the disbelievers and taking them as confidantes and close friends.
Abu Dawood (4832) and at-Tirmidhi (2395) narrated from Abu Saeed that the Prophet (blessings and peace of Allah be upon him) said: Do not keep company with anyone but a believer and do not let anyone eat your food but one who is pious.
Classed as saheeh by Ibn Hibbaan; classed as hasan by al-Albaani in Saheeh Abi Dawood.
Friendship and keeping company leads to love and approval, and it is not permissible to show that towards the kaafir.
This does not mean that there should be a complete cutting off of ties between Muslims and non-Muslims; rather she can visit her socially and when she is sick, and give her gifts, without loving her or taking part in her festivals, and her intention in visiting her and giving her gifts should be to call her to Islam. This is what our Prophet (blessings and peace of Allah be upon him) did. See question no. 23325
Based on that, you should explain to your daughter the guidelines on interacting with non-Muslims and help her to develop a feeling of pride in her religion and adhering to its commands, even if that goes against one's whims and desires. You should also discourage her from thinking of spending the night outside her home, because sleeping over in someone else's house is indicative of very close friendship, and we have stated above that it is not permissible for the Muslim to form such a close friendship with a non-Muslim. Perhaps she may be attracted to some of their ways and influenced by that without realising. The negative consequences of mixing too much with people who are not religiously committed are many, so how about mixing with people who are not of the same religion?
And Allah knows best.