Is it permissible for a woman to travel to visit her husband's family accompanied only by her mother, for a distance that takes 3 hours by bus, knowing that the road is safe and they will return on the same day, and that the father is unable to travel and she has no brothers?

A woman is not permitted to travel without a mahram. What the questioner mentioned does not justify this. Communication can be maintained by phone until it becomes easy for one of her mahrams to travel with her, or for the husband's sisters to travel accompanied by one of their mahrams. The mother's company on this journey does not change the ruling; rather, it increases the sin, because she herself also needs a mahram, and both of them would be sinful.