What is the Shar'i ruling on dealing with siblings who do not keep in touch with me, and some of them boycott me, because I refused to divorce my wife?

Muslims are required to foster harmony and love, especially among relatives. Your connection to your brothers, despite their estrangement, is good and a sign of faith, so persevere in that. We advise you to be gentle with them, to deal with them tactfully, and to strive for reconciliation. Your brothers have no right to force you to divorce your wife unjustly. If she is righteous, then keep her and treat her well.