Lol, hate to say it, but it sounds like she is just 8!! My son is almost 10 now and I think they all go through this stage. I think girls particularly have a lot of social pressure at this age and start breaking into cliques at school, etc.
I noticed that you start by mentioning she has Type 1 Diabetes- but I don't think that is really relevant to the issue. Certainly it should not be an excuse for rude behavior. If grandma is there a lot and is NOT discouraging this behavior, you need to have a firm talk with grandma. Ask her if she wants a mouthy brat for a granddaughter and explain how she might be (unknowingly) contributing to that. Tell HER that if things don't shape up, she may not be able to watch her granddaughter so often. She is an adult, after all, and should be able to control herself and her responses better than an 8 year old.
I'm not sure if taking away dance will help.It sounds like it is a good physical outlet for her as well as providing its own structure and discipline. When my son talked back, etc. we took away his Nintendo, no playdates etc.
I think that some of the responses below are pretty harsh. 'Punishment' can cover a lot of things. My son is one of the best behaved children I know, and although he got spanked a couple of times for serious things when he was small, I don't know how much difference it made in the end. Personally I would not let a book authored by Dobson into my house. I can be a good parent without that kind of influence!
But I am not advocating that you put up with back talk, either!! I like the 'toothpaste' idea about words that cannot be taken back. We always talked about the word 'hate' as in " I Hate You!" and how it is 'too big' a word for most situations. After we had this discussion a few times, my son never used the word again towards me or to complain about anything.
We made a firm schedule of chores and stipulated that they don't just have to be DONE- they must be done willingly and cheerfully. We had talks, over and over again, that attitude counts just as much as actually getting something done. Doing a task isn't really 'punishment' - but it is practical, keeps the kid busy and lets them know that you are in control of what goes on. If she doesn't do her chores and mind her manners, then she doesn't get to watch movies, go on playdates, etc. As she gets older and her friends are doing more and more these activities will become more important to her.
Eventually it sunk in. He is a little older now, a little more mature- and very very responsible!
BTW, he only exhibited this 'talking back' snarky attitude with ME. His teachers, aikido instructor, etc. always found him to be very polite and never snotty! They say kids are hardest on the people they feel safest with and this seemed like a huge test of that!! But like the 'terrible twos' the 'eight going on eighteen' as my fiancee called it, passed as well!! Good luck :)