Which of the two is more deserving of charity: the poor widowed sister who lives on social security and has two sons who do not give her money, or the poor widowed neighbor who has no income after her husband's death and has four young daughters?

If your sister is poor and has no one to support her, or if her provider is unable or unwilling to spend on her, then it is permissible to give her from the obligatory Zakat (definition) and voluntary charity. However, if your neighbor is poorer, then it is better to give to her, because the one in greater need is prioritized, even if they are not a relative.