What is the way to deal with a husband who continues to communicate with a female colleague at work, despite his repeated promises to cut off the relationship, which has led to a loss of trust, especially with children present?

The basic principle for a Muslim is soundness and to interpret their actions with good faith. It is obligatory to believe the husband when he denies having a relationship with the girl, unless proven otherwise, while noting that it is impermissible for him to speak with her except out of necessity. The wife must repel the whispers of Satan, avoid searching and tracking her husband, advise him to stay away from forbidden acts, remind him of Allah Almighty, and of the necessity to seek work where there is no intermingling, or to fear Allah as much as possible if he is compelled to work in a mixed environment. The wife's patience contains much good, especially with the presence of children.