What is the ruling on a wife’s actions of taking and using gifts and refusing her husband’s return to his home, knowing the purpose of these gifts, and what is the ruling on the silence of the wife’s family regarding this?

If a man takes his wife back during her iddah (waiting period), she is legally his wife, whether she consents or not, according to the Almighty’s saying: "And their husbands have a greater right to take them back." Documenting this in court is for the purpose of documentation only. Her refusal to obey you is a forbidden act of defiance (nushuz), so she should be advised to fear Allah and return to her senses. Mediation can be used to reconcile the matter, and if that does not work, the issue should be referred to a judge. As for what you gave her, it appears that it is not permissible for her to keep it, and you may reclaim it from her, as it was a gift for a specific purpose that was not fulfilled. It is preferable to refer to the Sharia court in matters of disputes.