Is it permissible for a husband to abandon his second wife and reside with his first wife if the reason for the abandonment is the second wife's father insulting him and reproaching him about her apartment, coupled with the wife's lack of firmness in her stance regarding her father's behavior? And what should be the duration and manner of this abandonment?

It is not permissible to abandon one's wife for a mistake made by her father, as Allah Almighty says: "And no bearer of burdens will bear the burden of another." The husband must provide a dwelling for his wife. If the wife agrees to waive her right to a dwelling, then there is no blame upon him. However, it is not permissible for her or her family to hold this against the husband.