Is the condition set by the wife's family that the husband provide a financial bond for her return, after she went to them angry, claiming mistreatment, a legitimate condition, and are they sinful for this condition? What is your advice to the couple and the family in this situation?

The wife's family has no right to obligate the husband to sign a financial bond or to prevent her from returning to her husband's house without just cause. The wife's obedience to her husband in this matter is more obligatory than her obedience to her parents. The husband should treat his wife well and fulfill her rights, and it is advisable for two arbitrators to intervene to reconcile between them.