Should the wife be informed about her husband's infidelity, given that he travels for adultery and some of his relatives are aware of it?

If the accusation is based on mere suspicion, it is not permissible, due to Allah’s saying: ﴿O YOU WHO HAVE BELIEVED, AVOID MUCH [NEGATIVE] ASSUMPTION. INDEED, SOME ASSUMPTION IS SINFUL.﴾ (49:12). However, if there is clear evidence of adultery, the person must do the following:

Firstly: Advise the person who committed adultery and remind them of Allah, and that their act is a grave sin. Secondly: If they do not respond, threaten to expose them or inform the official authorities or whoever can deter them. Thirdly: If that does not work, and there is legitimate evidence (four righteous male witnesses who observed the act), then it is obligatory to inform whoever can prevent the evil. It is stipulated that the testimony must be explicit and based on direct observation. Fourthly: It is not permissible to inform the adulterer's wife unless legitimate evidence (four witnesses) is available and it is known with certainty that informing her will remove the evil. Otherwise, informing her without evidence or with the expectation of destroying the family is not permissible.