wife took child to brazil. child is us citizen. no legal separation or court order in place. passport signed by both parents. what do i do?

This is a very complicated question and really would require direct consultation with an attorney experienced in these types of international custody cases. They are also very involved and likely expensive to litigate. You may have read about some of these cases over the past two years that involved court fights both here and in the other countries. One famous case involved a family whose child was held by a grandmother in Brazil, and that case took years of appeals before the child was returned. Another involved a mother who took the child to Spain, and Spain refused to honor the US court orders. Maybe you can check the news and find the names of the lawfirms that were involved in these cases.