Is a girl's distance from her married mother and leaving to live with her for work and independence—especially given her discomfort living with her stepfather—considered haram, despite her efforts to be dutiful to her?

If your residence away from your mother does not cause her loss or harm, and you are safe in your place of residence, then there is no blame upon you for that. You are not obligated to stay with her and her husband. However, you must strive to show filial piety to your mother to the best of your ability.