Is it permissible to continue in a permissible job, but which the questioner dislikes and feels anxious that her earnings from it might be unlawful due to her dislike of it and of her colleagues' behavior, or will leaving it cause her to fall into the sin of neglecting her family whom she supports?

Neither loving nor hating the work has any effect on the earnings. Rather, what matters is performing the work as required, ensuring it is free from forbidden acts or assisting in them. If these conditions are met, then the earnings are lawful. If the work adheres to Islamic guidelines, is free from forbidden acts, and no other option is available, then the advice is to remain in it and perform it as required. However, if the guidelines are not met or if it involves something forbidden, then it must be abandoned.