Is it permissible for a married woman to go out with her female cousins—without a mahram—to visit her other uncle’s house and stay overnight there, which is 20 kilometers away from her husband’s house?

If the distance covered by women is considered a journey (safar), then they are prohibited from undertaking it without a mahram. If it is not considered a journey, or if it is within the same town, then they are not prohibited from undertaking it alone or in groups, provided that temptation (fitnah) is safeguarded against. There is no harm for a woman to stay overnight at her paternal uncle's house if temptation is safeguarded against.