Is it permissible to work for a charity organization that is funded by lottery and usurious profits, knowing that the job responsibilities do not include direct participation in these transactions, and that the salary is paid from these funds, given the questioner's need for work and to support her ill mother, and her unwillingness to fall into disobedience?

The charitable society and similar bodies that receive prohibited funds, such as interest and lottery winnings, because they operate in good deeds and serve the interests of Muslims. Therefore, what the questioner receives in exchange for her work in the society is permissible, even if its source is prohibited money. If the society engages in lottery practices or deals with usury but also has other permissible income streams, then it is permissible to deal with it, albeit disliked.