Is it permissible to obey one's parents by boycotting the wife and her family and not visiting them, by preventing the wife from being taken to her family's home, and by not showing approval of the wife and her family, all due to family disputes, given the presence of two children and attempts at reconciliation from the wife and her family?

Your duty is to strive for your parents' رضا (satisfaction) without wronging your wife or her family. Holding your wife accountable for her family's misdeeds is an injustice in which obedience to parents is not permissible. You should try to convince them of her innocence and that there is no relation between treating her well and being dutiful to them. Treat your wife well and do not wrong her, and be good to your parents, and work to reconcile your family and your wife's family. If the estrangement is from your parents, then part of being dutiful to them is to guide them to the truth, prevent them from injustice, and not assist them in it.