Hi lisa6,
It seems to me that Kate has different ideas of what she wants from her relationship with you and your husband, compared to what you two are hoping for with her. Maybe you're finding out that she's not compatible with you. To some extent she seems to take advantage of your goodwill for her, but I can't tell how much of that is her having a different idea of how a relationship works. Also, I'm not sure how much she craves the kind of intimate time you would expect on a date. Maybe she doesn't need that very often.
I don't blame you for being upset, and I am inclined to suggest to you to break up with Kate, or at least dial down your amount of involvement with her, which you are already doing. You've tried to talk to her about your concerns and she has brushed that off as "nagging," so the only thing left is for you and your husband to decide whether you'll tolerate her frequent canceling of dates. If not, then breaking up seems to be the thing to do.
Sorry you are in this crappy situation.
Sincerely,
Kevin T.