What is the Sharīʿah's stance regarding a husband who has neglected his duties towards his wife and family, which led his wife to internet and chat addiction, then to developing admiration for a swimming instructor, along with her confession of hating her husband and the husband's desire for divorce despite his fear for the future of his two daughters?

The main reason for the problem is your neglect of your wife and children and your preoccupation with the computer and games, which led to an emotional void for her and pushed her to seek to fill it elsewhere. This resulted in her addiction to the internet and chats, and her admiration for others. Although a wife's mistake should not be treated with another mistake, the solution begins with you by fulfilling your wife's rights and satisfying her emotional needs, and by emulating the Prophet, peace and blessings be upon him. With your wisdom and patience, you can transform hatred into love and the desire for divorce into a commitment to harmony. As for the wife, she must fear Allah, strive for family stability, be a good wife, and adorn herself for her husband.