I just saw something on one of those discovery thing, like letting things like eye rolling slide, however name calling, telling you no and back talk is not allowed. Kind of that if she does it with a huff, to ignore the huff and not react, however do not tolerate disrespect either. Even with my younger kids I say "You are allowed not to like doing what I have asked, however it is important you listen to me"...
Consequences. Whether they are 3 or 13 make her responsible for her behavior. Respect is earned and she has none for you right now, meaning what you say, making sure you stand firm and don't allow it will help her find respect. If you ask her nicely to do something and she says "no", well then you say "excuse me it wasn't an option I asked you to do it, you can either do it without any sassing or you can have no tv for the rest of the week, your call".. period. No arguing, just that simple. If she calls you a name, look her in the face and say "that really is disrespectful and hurtful, I know you don't mean it however it is not going to be tolerated, do you have something you would like to say to me?" give her a chance to back up, apologize and say what she meant to say nicely.
If she doesn't, consequences. When you are doling out grounding, taking TV/Computer/phone priviledges just simply say "until you understand you are causing this to happen by disrespecting me then it will continue to happen, all on you". Be matter of fact, don't raise your voice and stay calm. Just letting her know it is her decision.
Picking on younger siblings happens, if is mean spirited or cruel again, consequences. She has to earn her nice things, fun times and you need to stand tough. Having your husband back you at every turn will help too, he is to stand behind you when you dole out the punishment and support you! Whe she back talks you in front of him have him stand tough and not allow it either!
Good luck, I dread the teen years but I think being consistent is crucial at 3 or 13 and like I say all the time "mean what you say and say what you mean" no idle threats, no three chances, just it is what it is, her choice period.