What is the ruling on a woman working in a nursery affiliated with an association managed by a man?

A woman's work in a nursery is permissible if it does not lead to her being alone with a non-mahram man (khalwa) or to fitna (temptation/strife). If it leads to any of that, then it is not permissible. Khalwa is the gathering of a man and a woman in a place where they are safe from anyone entering upon them, or where their persons are concealed from people.