Is the wife of a half-brother considered part of the rahim (kinship ties) that must be maintained, and what should I do regarding her lack of communication with me or my brother?

The wife of one's brother is not considered a close kin (رحم خاصة), but she is kin in a general sense (رحم في الجملة). Maintaining kinship ties is a great good. Therefore, we advise the sister to maintain ties with her brother's wife, to overlook her mistakes and shortcomings in her rights, and to meet her with connection and fulfilling her rights. We also advise her to maintain ties with her brother's kin, even if he severs them, so that she may be among those whom Allah describes as having patience and a great fortune, as confirmed by His Almighty saying: ﴿Repel [evil] with that which is better, and thereupon the one whom between you and him is enmity [will become] as though he was a devoted friend. But none is granted it except those who are patient, and none is granted it except those who have a great portion [of good].﴾ [Fussilat: 34-35].