Is the questioner's position of her mother not going to her manager, who is harassing her sectarianly, correct, after she put her trust in Allah and refused to beg someone who does not deserve respect, despite her need for her salary?

If it is hoped that your mother's visit to the manager will avert his harm from you and end the problem, and there is no humiliation for her in it, then there is no objection to that. This is part of taking lawful means, just as Islamic law has permitted good intercession; as Allah Almighty says: (Whoever intercedes with a good intercession will have a share of it) An-Nisa/85. And the saying of the Prophet, peace and blessings be upon him: (Intercede, and you will be rewarded). So consult those with experience, and if good is hoped from this visit, then do not prevent it.