Is it permissible to travel with "non-mahram" relatives and stay with them in one dwelling, knowing that the wife wears a niqab and does not wish to appear before them, and that not traveling might incur the parents' displeasure?

Obeying parents is obligatory in what is good and permissible, but it is not obligatory in acts of disobedience or in what harms the child.

If the dwelling that the mother rents has shared facilities and exposes the wife to seclusion (khalwa) with or suspicious mixing with non-mahram men, then the mother's command to travel with the wife and reside in this dwelling is not obligatory to obey; rather, it is impermissible.

Similarly, it is not obligatory to obey the mother's command to travel with them alone if it would leave the wife in an unsafe situation.

However, if it is possible to travel with the wife and reside in a dwelling with private facilities, or if it is possible to leave the wife in a safe place, then it appears that obeying the mother in this regard is obligatory, even if there is a tolerable difficulty.