Is divorce considered valid merely by intention, and how is a wife divorced while she is at her family's home without knowing whether she is ritually pure or not, and what should be done in this situation?

Divorce does not occur merely by intending it; rather, it requires verbalization or written declaration. Therefore, the wife remains under her husband's marital bond as long as he has not pronounced or written down the divorce. Divorce is not a trivial matter due to its consequences, such as the disintegration of families, which brings joy to Satan. Allah has permitted divorce because people sometimes need it.

The husband should not rush into divorce; he must be deliberate, for Allah Almighty said: (But perhaps you hate a thing and Allah makes therein much good.) An-Nisa/19. Thus, Allah encourages the husband who dislikes his wife to keep her and promises him abundant good in return.

As for the problem of the wife's neglect of cleanliness, it can be remedied through advice and guidance, and her family can be sought for help. The first step is to return the wife to her home and try to mend the situation. If her condition improves, then praise be to Allah. Otherwise, the husband has lost nothing, and he can then ascertain the true state of affairs, and he is more discerning about what is best for him.