Is the wife sinful for moving to her family's home after her husband's death, and for leaving the marital home where her husband had advised her to stay to raise their son, knowing that her mother is alone and she cannot leave her?

You must remain in the marital home until the end of the 'iddah (waiting period) of death, and it is not permissible to leave except for a legitimate reason. After the 'iddah ends, it is not obligatory to remain in the deceased husband's home, nor is it obligatory to obey his bequest to stay in the house. Rather, you must stay with your mother and care for her as long as she needs it, for the right of the mother is great, and honoring her is among the most obligatory duties, especially in her weakness, according to the Almighty's saying: "And your Lord has decreed that you worship none but Him. And to parents, show goodness. If one of them or both of them reach old age with you, do not say to them 'uff' [a word of disrespect] or repel them, but speak to them a noble word."