Is it permissible for a husband and wife to agree upon the husband's travel to work as a diplomat, with the wife's knowledge of the possibility of her being compelled to intermingle with foreigners at parties (by shaking hands or seeing them consume alcohol), and with the presence of children who are feared to be influenced by these societies, especially since refusal would forfeit a significant financial opportunity?

It is not permissible to attend or organize parties that include religiously forbidden acts such as intermingling (between sexes), revealing of 'awrah (private parts), drinking alcohol, and music. If one's job obliges him to attend such parties, he is not permitted to do so, especially if the travel is not mandatory. Saving money does not justify committing forbidden acts. Whoever abandons something for the sake of Allah, seeking His pleasure, Allah will compensate him with something better and provide for him from where he does not expect, as stated in His (Allah's) saying: "And whoever fears Allah – He will make for him a way out And will provide for him from where he does not expect."