Is it permissible for the husband to send his wife to her family's home to observe the waiting period there after her repeated infidelity, and does this fall under the Almighty's saying: "unless they commit a flagrant indecency" from Surat At-Talaq?

A woman's engaging in sinful relationships with foreign men is a grave transgression and a dereliction of her duty to her Lord and her husband. If she does not repent, then divorcing her is better for her husband, because she would not be chaste. The original ruling is that a woman who is revocably divorced (ṭalāq rajʿī) must observe her waiting period (ʿiddah) in the marital home, and it is not permissible for her to leave it or for her to be expelled from it, unless she commits a clear act of immorality, such as disobedience (nushooz) and adultery. What this woman did is not included in this, so it is necessary for her to remain in the marital home until the waiting period ends.