In the workplace one should always be polite, efficient and effective. This does not equal being friends with all or any of your coworkers. In a perfect world it would be pleasant and wonderful to have positive friendships with the people we work with but sometimes we just need to be professional and not cross over into friend country. Since she is immature and/or crazy, my personal motto is to leave the crazy people alone. I don't entertain relationships with crazy people. I maintain my professionalism, keeping things as simple as possible, daily hellos and good byes and discussions of the work if necessary but there is no unnecessary conversation with unstable people. No goo can come from it.
Your husband needs to make a decision about what he is going to do or not do in regards to his unstable coworker and then do just that while maintaining a exceptional level of professionalism and work ethic. As his wife your job is to encourage him but don't throw yourself into the mix. Doing so would be unprofessional on your part and I I know this may be a hard thing to ask of you but it must be done. I hope this helps.
UPDATED
Just read your post. Siince she doesn't work in his department there is no need for him to be nothing but coordial but nothing more. So no more cards, gifts or the like and he definitely shouldn't be accepting gifts from her and all of this can be promptly squashed especially since she is being weird with him now anyway. My concern as a wife would be that my husband would be entertaining this kind of drama in his workplace which could effect his pay and job. Not a wise move, I think.