Should the husband abandon his brother and sever ties of kinship with him, despite his brother's denial, given that the husband believes his wife's claim that she was subjected to forced adultery by the brother?

The crime ofzina (adultery/fornication) is not established except by one of two matters: the perpetrator's confession, or the testimony of four witnesses who saw the act ofzina. Your brother's situation does not fulfill either of these two conditions, so it is not permissible to accuse him.

As for your wife, her confession ofzina does not necessitate the prescribed punishment (hadd) upon her, because she was coerced, and prescribed punishments are averted by doubts. As for her accusing your brother ofzina, if she cannot prove it, she deserves the prescribed punishment for slander (hadd al-qadhf) if your brother demands it.

Islam imposed these prescribed punishments and stressed the need for witnesses to preserve honor. Caution must be exercised regarding a woman being alone with her husband's brother (hamu) because this can lead to temptation.

It is not obligatory to sever ties with your brother due to the lack of proven accusation; rather, he should be advised and admonished.