You're saying the verbal side has developed over the past 2 or so years. It isn't explicitly stated, but I take it that this has developed at the expense of physical acting out? Has the hitting and pinching decreased linearly with the increased verbal abuse? I'm asking, because that's the way it tends to go, and I think it is usually instructive to get a sense of that development: with the very young children, kicking and biting may be the only tools they have for expressing their discontent. As they develop, so does their tool belt, and they acquire more sophisticated modes of expression. The end goal you're hoping for is the ability to identify their own needs and communicate them in a constructive manner, and satisfy them through civilized discussion. That's a big ask of a six year old, though.
I'm not saying any of this in defense of verbal abuse. Abuse is abuse. But if what you're witnessing is indeed, as is often the case, the acquision of one means of abstaining from physical violence, I think it is helpful to recognize that, rather than just viewing it as an additional means of causing hurt.
As with any abuse, your priority must be to side with the victim to minimize harm. Having taken care of that immediate concern, and moving on to putting an end to further harm, however, your focus must be on the aggressor. It is their behaviour that must change; not the victim who needs to build up resilience, as others have noted.
To that end, I stress that all bullying must be taken seriously, and that obliges us to look at what is effective, and not satisfy ourselves with what feels intuitively like the right thing to do. Applying punishment may feel effective, but it has been shown to be really poor.
I am personally vehemently opposed to time outs. We are a social species; solitary confinement is one of the harshest punishments there are, and it is heavily regulated in most penal systems. Communicating that our children are not worthy of our love and attention unless they act in a way that pleases us is a terrible lesson to teach. Furthermore, acting from a place of authority teaches that those who are older have the right to treat those who are younger in whichever manner they see fit, which is exactly what you see perpetuated in your older daughter's behaviour.
You want to teach the exact opposite lesson: compassion and cooperation. In order to do that, you need to model it. The fact that you describe how she refers to not having broken any rules also indicates to me that you are currently having a very rule-based focus on behaviour, in which case this is a natural and expected response. Forget the rules, I say, and get down to core principles. There are no loopholes in "be nice" the way that there are in "X and Y are forbidden words". There is room for interpretation, yes, but you want them to learn how to navigate nuance. Those will be meaningful discussions that your children will grow from, which is not the case with the mindless discussions on whether Z should also be counted as a forbidden word. When a set of house rules govern behaviour, we all look for escape, and hypocritically, we the adult arbiters of that law will tolerate our own diversions from the rules as reasonably motivated to a greater extent than that of our children.
Now, you're asking for how to deal with this behaviour, but to find the very best and most effective answer to that question, which I think the immediate nature of your situation obliges you to, you need to go deeper, and enquire about why it occurs in the first place. Rather than just laying down the law, ask your younger daughter about her behaviour. Why is she doing this? What is she looking to achieve? Kids don't act out without a reason. They may have poor reasons, or good reasons acted on poorly, but they're not acting entirely at random.
"I notice that it seems difficult to you to be nice to your younger sister. What's up?" And then really listen. Don't judge, don't correct, don't intervene. Listen. Dig deeper. She will never be open to accepting your solutions until she feels heard in her own distress. Obviously something is distressing her, even though the little sister may well have nothing to do with it. She is probably just innocent collateral damage.
Perhaps that leads to some revelations, perhaps it doesn't. Either way, the listening will have been useful. But quite likely, if she truly feels seen, you may be able to unearth something that is bothering her. And you may be able to get her to go along with another mode of expressing that.
And you need to analyze not just the incidents that happen, but the circumstances surrounding them. What is weighing on the younger daughter when she cannot be nice? Because kids do well if they can. All children would ideally want to be constructive members of their family or peer group. It is much more efficient to try and help her by analyzing lagging skills rather than assuming a lack of motivation. The ALSUP is a good place to start, if you don't know what to look for.
Perhaps she is too tired or hungry at a particular time of day to be able to keep from acting out? I'm sure you know most of us don't always have access to our ideal responses, but are affected by mood swings entirely unrelated to the conflict at hand. Perhaps she doesn't know how to constructively engage with her sister when she wants to interact. Perhaps she doesn't know of a more effective way to get your attention? Perhaps she has difficulty channeling her own hurt into an acceptable outlet.
Often, backing up to 30 minutes before an incident will be enough to find useful clues to what the triggers were, and doing that often enough will hopefully also reveal patterns that were not immediately apparent.
The best course of action will depend on what the problem actually is. You need to find that out together with her. But the most effective solution is always to help, never to punish. And as I said, bullying needs to be taken seriously. You cannot allow yourself to resort to knee-jerk reactions.
