Is it permissible to give charity to a neighbor who is not considered poor or needy, whose husband provides for her within limits, which sometimes leads to her and her children being deprived of some basic necessities, despite her husband's financial capability?

It is permissible to give supererogatory charity to the rich, but the needy are more deserving of it. If a woman's husband falls short in providing for her due to incapacity or negligence, and he cannot be compelled to do so, then she and her children are considered among the indigent. It is permissible to give Zakat (definition) to them, and it is even more appropriate to give them supererogatory charity, which would be an act of devotion.