Is the decision to travel for work to Saudi Arabia, leaving the children temporarily with the husband's mother, in light of the husband's unemployment and accumulating debts, considered wrong or right?

It is obligatory for the husband to financially support his wife. The wealthy wife is not obliged to spend from her private money unless she volunteers, nor is she obliged to earn for sustenance. If the husband becomes insolvent, the wife has the right to refer the matter to the judiciary or to be patient. You are not obliged to earn or travel, but if you undertake a permissible job to provide for yourself, your husband, and your children, it is an act of kindness, provided that the work is permissible and free from শরعي (Shari'ah) violations, and that you do not travel without a mahram except out of necessity. As for residing in a country of travel, a mahram is not required for it, but it is stipulated that you feel safe for yourself.