Put aside the reality that the DOJ wouldn't do anything even with a hundred million signatures because no federal law has been broken and it would be contrary to the Constitution. Besides that, those signing the petition should think about what a slippery and dangerous slope it would be for the government to start investigating every percieved harm in society. As wearewatchingyouman pointed out, people unfortunately commit suicide for a lot of reasons. Why not criminalize adultery, being a poor parent or child, unkindness to co-workers, or the many other things that have led to suicide in some cases? Why not force everyone to be nice to everyone else under penalty of prosecution? Wouldn't anyone who turns someone against a friend so that they "shun" their former friend be part of some conspiracy to violate human rights?
Think also about the right to speak out critically that we take for granted in free societies. Essentially, the petition wants to criminalize the WT's criticism of former members and their collective decision to shun the former members. Why would the government then not have to investigate anyone who speaks out critically toward politicians, businesses, celebrities, or religious groups (any "Anti" movements come to mind?) to see if the criticism is justified? This is why the better way to combat shunning and breaking up of families is to publicize it and expose their double speak for what it is.