R.F.
I had three children in five years. I completely understand you being overwhelmed AND the desire to instill manners and respectablity. MANY years ago, my husband & I attended a parenting seminar and came away with several "jewels". All five of us are "Type A", domineering personalities. That combination made for some terrific battles. One jewel we received is to try to catch the child doing something good and praise them for that good deed. Even if it just sitting with their mouth closed while watching. Basically, the things we expect them to do -- praise them when they do it. We found this worked like a charm on two fronts -- one, it caused the kids to do more of what we wanted in the first place AND second, it stopped my screeching so much! Now, it didn't solve everything; but, it was a great start.
Your 9 year old is simply being a result of her environment. You have rules she hates and her grandparents don't have rules. She's confused, frustrated and very angry and she's showing her emotions by defying your rules. I encourage you to stand your ground. It sounds like you are doing more for her than anyone else. But, as a mother, you have a thankless role.
Posting the rules was another jewel we gained. We had age-appropriate rules, gave "tickets" when we caught them doing good things, took "tickets" when they were disobedient. The "tickets" could buy pre-arranged treats -- a small toy, extra TV/computer time, McDonald's meal, etc. You get the idea.
Another thing I learned MANY years ago, is that a child will strive for attention -- any attention, good OR bad. Your 9 year old is desperate for attention. Help her to earn the good kind by prasing the few things she does right.
Hang in there. Motherhood is a really tough job; but, the rewards are extreme!!
R.