Will the wife be sinful for neglecting her home and feeling indifferent, especially since her husband does not care about the cleanliness of the house, and what is the best way to deal with a husband who is inclined towards her neighbor and deludes her into thinking that her feeling is mere illusion?

Reminding the questioner sister of her individual responsibility before Allah for her actions. It is not permissible for a wife to withhold her husband's right from him or neglect her home under the pretext of his disobedience, as this does not negate his right. Neglecting the home can lead to the husband's alienation. The best way to deal with the husband is to obey Allah concerning him, fulfill one's duties towards him, and advise him with gentleness. It is also necessary to advise the neighbor and warn her against betrayal if there is any illicit behavior between her and the husband.