Is what the brother's wife does by preventing her husband's brothers from seeing her children Haram (forbidden), Wajib (obligatory), or Ja'iz (permissible)? And what is the ruling on the husband obeying her in severing ties of kinship out of fear of her? And is there a Hadith that clarifies the punishment for that?

What your brother's wife and your brother are doing by preventing you from seeing or contacting your nephews is a grave mistake and is impermissible if there is no legitimate religious reason, for cutting off kinship ties is one of the greatest sins. Allah Almighty says: (Then, is it to be expected of you, if ye were put in authority, that ye will do mischief in the land, and break your ties of kith and kin? Such are the men whom Allah has cursed for He has made them deaf and blinded their sight) {Muhammad: 22-23}. In Sahih Muslim, it is narrated on the authority of Aisha, may Allah be pleased with her, in a Marfu' hadith: "The womb (kinship) is suspended from the Throne, saying: 'Whoever keeps ties with me, Allah will keep ties with him; and whoever severs ties with me, Allah will sever ties with him.'" In the Sahihayn, the Prophet, peace and blessings be upon him, said: "No severer of ties will enter Paradise."