Is it permissible for a wife to remain with her husband who was religiously committed then committed adultery several times, and claimed repentance after confessing to it in front of her and in front of his family, given her fear of not being able to support her four children in the event of separation?

Love for the sake of Allah and hatred for the sake of Allah are among the strongest bonds of faith. Therefore, one should hate the disobedient person for their disobedience, but only to the extent of the sin, not with absolute hatred, as long as the foundation of faith remains. If the disobedient person repents with sincere repentance, the signs of which are rectitude and remorse, then you should change your perception of them. Sincere repentance demolishes what came before it, and all sins, even polytheism, are forgiven through it. Allah accepts the repentance of His servants, and the calamity is not in making a mistake, but in persisting in it. The occurrence of adultery or any other immorality by one of the spouses does not invalidate the marriage contract. It is advised to be patient and strive to counsel them, but if they do not reform, you may seek a divorce, though it is not recommended for the sake of the children. One should not spy on them or force them to confess a sin, nor should they expose themselves; rather, they should conceal themselves, as the Prophet (peace and blessings be upon him) said: "Whoever is afflicted with any of these abominations, let him conceal himself with the concealment of Allah."