Is it permissible to work in a nursing home in the West that houses both men and women, or in food stores that sell pork and alcohol, given a dire need for money and the unavailability of other alternatives?

Both mentioned jobs contain Sharia prohibitions. However, if the need for the work reaches a level of necessity that cannot be dispensed with, then one may work to the extent that this necessity is met. This must be done while weighing the two jobs to choose the one with the least sin, and it appears that working in the nursing home is that one.