"....Thius will really be the first time my husband has experienced the birth of his child, since he was not living here last time, and I want it to be memorable to him. They do not get along very well (my friend and husband). I know I will be totally stressed if she comes over, and I really want it to be a family time for my husband, daghter, new baby and myself, since he has little time off. But she is dead set on coming over....."
Sorry, but I think it is incredibly rude of your friend to try and force herself on you, at a time when you just want it to be your husband and daughter there. Have you come out and told her that you just need some time with your husband, but that she's welcome to come over afterwards? I would tell her that your family and your husband's family will be there for the first couple of weeks helping out, but that you could "really use her help" a few weeks further down the road as that will be when you're the most stressed, or something like that.
You say she's very, very, easily offended/hurt but she doesn't seem to care too much about what YOUR wishes are-----only hers. No matter what you say, she's probably going to be offended but sorry, if she's willing to give up a life long friendship over something like that, she's not a true friend.