Is it permissible to punish the soothsayer who caused the divorce, and take revenge on him, or should one strive to bring the wife back and rescue her from this path, or move on and marry someone else?

Do not concern yourself with taking revenge on the soothsayer. Entrust your affair to Allah, for He gives respite to the oppressor but does not neglect him. And whoever does not receive their recompense in this world will receive it in the Hereafter. The most important thing is your children and their mother's situation. Strive to advise your ex-wife and reach an understanding with her to take your children, and seek help from relatives and respected figures. Rely on Allah, think good of Him, and be patient, awaiting relief.