Would the wife be sinful, and would her family be angry with her, if she returned to her husband's home (the husband's father's house) after a divorce and reconciliation, despite her agreement and desire for that, and her family's refusal on the pretext that an independent home is obligatory?

It is the wife's right to have independent housing, and her family has no right to interfere as long as she is content with living with her husband's family. Obedience to the husband takes precedence over obedience to parents, as Ibn Taymiyyah said: "When a woman marries, her husband has more authority over her than her parents, and obedience to her husband is more obligatory upon her." However, she must still honor and be kind to her parents.