What is the ruling on a man remaining with his wife whom he does not desire due to her lack of beauty, while fearing to wrong her, being unable to marry another, or to divorce her because of the presence of children and her intense love for him?

The problem is financial, not related to a second marriage or divorcing your wife. If you are not financially capable, then hold on to your current wife. Polygyny is permissible if financial capability is available, and it is easier for a woman than divorce, especially with children present. Look at the issue from another angle: beauty is not everything, and good conduct is more important than appearance in the long run. You might marry a beautiful woman who has bad conduct. Be objective and do not burden yourself with what you cannot bear, for there may be much good in what you dislike. Remember the Prophet's advice: "Succeed with the religious woman, may your hands be dusty."