What is the ruling on the head of a household traveling for work when he is not strong enough to resist temptations, and his wife does not wish for him to travel because of the children's need for his Islamic upbringing, which cannot be achieved without him? And what is the permissible duration of absence?

It is permissible to travel for work or other purposes, and it may be necessary for earning a livelihood, unless it results in harm or a Shariah-forbidden act, such as neglecting children or the wife; otherwise, it is not permissible. The period during which a husband should not be absent from his wife without her permission and consent is more than six months.