Yeah, that is a very tough situation. It sounds like you are doing the "right" things. It seems that one breakdown is that she doesn't have enough trust in you to believe you are not being nasty. Sometimes this is due to people reflecting their own feelings on to others. For example, she may see you as acting fake because if the situation were reversed, she may try to act fake. I think all you can do is to keep trying and hope she understands you are sincere at some point.
It has got to be frustrating having your husband love someone who is acting this way. But it is hard to stop loving someone. He is probably hoping that there is a way for things to work out. It sounds like if he broke up with her, you would still have to deal with her in your life.
It seems that since you have to keep dealing with her no matter what (since you have to work with her), I think all you can do is to be sincere and hope she comes around to see that she has been misjudging you.
Sorry about your situation.