Is working in nail care for non-Muslim women permissible or forbidden, taking into consideration the severe financial need and the difficult family situation?

It is not permissible to beautify the nails of disbelieving women, just as it is not permissible to beautify women who display themselves immodestly, because it involves cooperation in sin and aggression.

However, it is permissible for you to work in beautifying the nails of disbelieving women if your father or son is in need of financial support and there is no one else to support them, because what was forbidden to prevent a means to an evil (sadd al-dhari'ah) is permitted for a predominant benefit.