Is it permissible for a Muslim to move to a permissible job in Medina, despite his mother's objection, especially since his current job is forbidden?

You must abandon the forbidden work and repent to Allah. As for traveling for permissible work without your mother's consent, it is permissible if travel becomes necessary due to the unavailability of permissible work in your country that can sustain you and those dependent on you. In such a case, her obedience is not obligatory, as obedience is only in what is good and permissible. However, if permissible work is available in your country that meets your needs, then do not travel without her permission.