How should one deal with a conflict between the essential and the complementary objectives [Maqasid], and is it permissible for Muslim women to work in government institutions without hijab if that is for the preservation of wealth, one of the essential objectives? And what does "preservation of wealth" mean within the essential objectives?

Preserving wealth is an essential objective among the five necessities. However, acquiring or preserving wealth does not mean working in any job, even if it leads to committing forbidden acts, such as uncovering one's awrah (intimate parts) or abandoning prayer. If a Muslim woman is compelled to uncover part of her awrah to work in a job she cannot find otherwise to sustain herself, then there is no sin upon her, because necessities permit the forbidden. The preservation of life is a greater concern than the harm of uncovering the awrah. As for abandoning prayer, necessity is not realized unless the situation reaches a point where even gesturing in prayer is prevented, or one is coerced into engaging in something that contradicts prayer. The distinction between the essential (ḍarūrī), the need-based (ḥājī), and the beautifying (taḥsīnī) is generally in terms of rank. This does not mean that everything related to wealth takes precedence over other matters. For instance, if a Muslim were given a choice between usurping a small amount of money and uncovering their awrah, it would not be permissible for them to uncover their awrah.