Is it permissible to take gold from one's wife before her travel to Egypt and divorce her there, while giving her all her rights, knowing that there are signs of greed and exploitation from her family?

If the gold is registered in the list of movables, then hold onto it until you hand it over to its owners or obtain a document from your wife confirming it is in her possession. However, if it is her property and not registered, do not prevent her from traveling with it. It is advisable not to rush into divorce and to strive for reconciliation as much as possible, as divorce is disliked in Islamic law and should only be resorted to when reconciliation becomes impossible.