Is it permissible to divorce one's wife based on suspicions of her infidelity, without physical proof, and how can this situation be resolved?

It is not permissible to accuse a wife or anyone else of immodesty without clear proof. The Shari'ah has emphasized the sanctity of honor and prohibited delving into it without right. It is not permissible to accuse a chaste person of adultery unless there are four upright witnesses, otherwise, the accuser is subject to punishment and their testimony is rejected. Allah says: (And those who accuse chaste women and then do not produce four witnesses - lash them with eighty lashes and do not accept their testimony ever after. And those are the defiantly disobedient) [An-Nur:4]. It is obligatory to conceal a Muslim's wrongdoing if they commit an indecency, unless there is a valid benefit [in disclosing it]. The mere presence of a man inside the house does not necessarily imply the wife's betrayal. If no evil has been apparent from the wife, then she should be returned to the husband's marital bond. It is advisable not to be absent from family for long periods, even if it is at the expense of financial gains, due to the psychological happiness and moral chastity it provides for the family.