Is it permissible for a man to travel with his wife's sister a four-hour distance in public transportation without a mahram for her, knowing that she will travel alone if he does not accompany her? And would he be sinful by accompanying her? And is it permissible if his wife (her sister) travels with them?

A woman is not permitted to travel except with a mahram. The sister's husband is not a mahram, so she is not allowed to travel with him, even if her sister (his wife) is with them. This is unless the travel is obligatory, such as for Hajj or Umrah, or due to a compelling necessity or urgent need where she cannot find a mahram; in such cases, it is permissible for her to travel with them, as they constitute a safe companionship.