Is it permissible to spend the night at the in-laws' house when visiting them, knowing that the mother-in-law insists on it and the wife is only comfortable in her parents' home?

There is no harm in staying overnight at the wife's family home if there is no Shariah-prohibited act involved. However, if the father forbids his son from staying overnight, it is obligatory to obey him if he would be hurt by his disobedience, unless the hurt is merely due to the father's foolishness. As for the wife, she may stay overnight at her family's home. It is possible to satisfy everyone by both parties visiting, and staying overnight where the father approves.