Who is the religiously responsible guardian of the wife after the death of her husband: is it her husband's family or her own family, knowing that her family is still alive and capable?

The responsibility for a woman after the death of her husband falls to her own family (her guardians, such as her father, brothers, and paternal uncles) in the order of the inheritance عصَبات (agnates), not the husband's family. As for her maintenance (nafaqah), it is from her own money if she has any. Otherwise, it falls upon the closest of her guardians (her son, then her father, then her brother). The husband's family is not obliged to provide for her maintenance except as a voluntary act of charity and kindness.