Is it permissible for a woman to wear a large hat to cover the front of her head and a large hair clip ("toka") to cover the back of her head, in a work environment that prohibits the hijab but allows hats?

The hijab (definition) is a religious obligation, and it is not permissible for a Muslim woman to remove it for work or any other reason, nor is it permissible to compromise on it. Allah has promised the righteous that He will provide a way out for them and sustain them from where they do not expect. Therefore, it is obligatory to leave any work that necessitates removing the hijab, unless there is an extreme necessity that cannot be overcome except by continuing in it, such as having no one to support her financially. In this case, only the amount necessitated by the necessity should be uncovered, and the job should be left immediately once the necessity ceases. What the questioner mentioned about wearing a cap and a hair tie is not a legal hijab, but it covers some of the hair, so she should wear it in cases of necessity.