Is it permissible to marry a second wife and leave the first, given the presence of children between the spouses, and knowing that the first wife refuses divorce and polygyny, and has recovered from her illness that prevented conjugal relations? And is the first wife entitled to hit the second wife?

We ask Allah to ease your affairs, relieve your distress, and mend the relationship between you and your wife. You should make abundant supplications. Since your wife has recovered and desires to mend the relationship, strive to accept her, for it may become easy for you. Among the things that aid in this is considering your offspring and their well-being, as harmony between you will help in their good upbringing, while separation might lead to their ruin. As for your second wife, you may reconsider her if you wish, and your first wife has no right to prevent you from doing so. However, do not proceed with this unless there is an overwhelming benefit.