People really do irritate me at times, where is the logic in spoiling one grandchild and not the rest of them!!! Seriously unfair, I would have to say something about it to her, as she is just getting away with it!!! I would explain to her that your child and yourself feel hurt by it.
As for the daughter, I can see a slight resentment, but dont feel bad for that, you havent caused this! Just because you may feel this, it doesnt mean that you dont like her...maybe you should try taking your "daughters" out together, for a girly day, shops, cinema and maybe something to eat after, you will get to know her a bit more by doing this and not only that, your daughter wont care as much when she comes round boasting about where nanny has taken her as she would have been out enjoying herself too. Another thought on the matter, when this girl comes round boasting, do you not feel that she may be resenting the fact that you are a family unit? Your doing everything right, but seriously, try spending some time with the girls together, and if you havent got the money for days out etc, put make up on them and do there hair, anything glittery and pink and im sure they will be happy!!!! Best of luck! x