All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
Firstly, we would like to point out that the wife should be keen on giving the benefit of the doubt to her husband and her protective jealousy over him should be moderate. She should avoid excessive jealousy and not misinterpret his actions and have bad thoughts about him. This causes nothing but heartbreak to the wife and could trigger disputes and bring about undesirable discord and perhaps divorce. Please refer to Fatwa 90757. It is a good thing that you mentioned that your husband didn't do anything inappropriate with that girl. If you see him doing something wrong, you should give him advice in a kind and gentle manner.
All of the girl's actions do not necessarily derive from bad intentions. You should give her the benefit of the doubt as well. As for this girl's negligence in observing the proper Hijab or her constantly being around men, she should be sincerely advised about it. Tameem Ad-Daari related that the Prophet said: “The faith is sincere advice.” [Muslim] Advice should be given in a kind and gentle manner. Hence, that girl should be reminded that she is in an Islamic organization whose members should be good and pious people since people normally have good expectations of them and look up to them. For further benefit, please refer to Fataawa 84485 and 159283.
As for quitting work at that organization, the decision should be based on the greater general good. There is a great interest in women staying in their homes, so they should do so unless it clashes with a greater general good. Allaah The Exalted says (what means): {And abide in your houses and do not display yourselves as (was) the display of the former times of ignorance. And establish prayer and give Zakah and obey Allaah and His Messenger. Allaah intends only to remove from you the impurity [of sin], O people of the (Prophet's) household, and to purify you with (extensive) purification.} [Quran 33:33]
Allaah Knows best.