Find positive ways to redirect her. Touch, get close, and use a calm voice when you prompt.
In that situation for instance, say "I am glad you noticed the crumbs under the cushions." Get close and touch and say "Please help me clean them up" or (if you need an additional incentive) "If you will help clean them up, we can do something fun after".
Try a few prompts, don't repeat them more than 3 times, keep calm, don't raise your voice.
Learn about the Patterson Coercive Cycle
, and use the recommended practices to avoid it:
In general, focus on the behavior you want. Catch he doing good and give her positive attention when she is kind to her brother. When giving positive attention: do it immediately when or right after the behavior occurs, get close, touch, be enthusiastic (scale the enthusiasm to the kid, some like a lot - others not so much), don't caboose criticism on the end, do it often at first (lots of reinforced practice at first is the key).
Use a Kindness Chart
You don't have to use praise, all types of attention are reinforcing. Show her you noticed by saying what you saw, do a running commentary when you like what you see her doing, show interest by asking questions, show gratitude, show admiration. If you use praise, use specific praise that describes the praiseworthy behavior, not generic praise like "good job".
As you are finding, out time-out can be difficult to use. Tend toward sending the both away for 5 minutes if there is a dispute rather than blaming one (but that might not be appropriate in all cases). Only use time-out for aggression and try other options first. Never threaten time-out, just start it when appropriate, be calm, don't talk much when getting it started,
You can train time-out with pretend time-outs where you give positive attention or points on a reward chart for a well executed time-out. Start with short time-outs and build to one-minute per year. Time-out will work as well, even if you give social or tangible reinforcment for a well-executed time-out. Use this approach to avoid defiance of time-out.
Getting time-out to not be counter-productive with a defiant kid is a pretty elaborate process.
Most of these ideas are from the book Kazdin Method
. Learn more and use other methods for that book.
Use collaborative methods from the book Incredible Years
, never give up on collaborative methods even if they don't work at first. Use them instead of rewards and punishment when you can. They are key to a good longer-term relationship with your kids.