Is a wife entitled to ask her husband to travel this year without him and without their parents, due to her psychological state, knowing that she usually travels with his parents most of the time?

There is no objection to a wife asking her husband to travel without his family, as it is not obligatory for him to travel with his parents every time. If the parents live in a separate house and have someone to care for them, then traveling only with the wife and children is better for strengthening the marital and family relationship.