What should a wife do with her husband who eats in Ramadan and refuses to fast, and is it permissible for her to remain with him when there are children?

If the husband eats during the day in Ramadan (definition) due to a legitimate excuse, such as illness, there is no blame upon him. However, if he does so without an excuse, he is committing a grave sin, and one should continue to advise him gently, supplicate for his guidance, and seek assistance from good people. If he repents, then praise be to Allah. But if he persists, the wife has the right to seek divorce due to his transgression. However, if they have children, patience and continued advice are more preferable, and she should not seek divorce unless it is clearly in her best interest to do so.