You need to stop thinking about it in terms of "bad behaviour = always and only negative reinforcement, good behaviour = always and only positive reinforcement". That works for dogs and lab rats, but children are people and people are more complex. It also works on young children because young children inherently want to please you (even if they don't always show that - they do have the desire to, it's instinctive, not pleasing mum + dad = get kicked out of the tribe and death) But that desire to please you lasts until they hit adolescence, suddenly they don't want to please you any more, in fact they have a vested interest in striking out on their own. So if everything up until that point has been centred around your approval/acceptance, you will find that it begins to fall apart.
That's hardline. In reality I don't know many parents who literally operate under these rules. But it's worth bearing in mind - every behaviour is a reaction to something. I find thinking in terms of limits and boundaries is much better than trying to label things good/bad behaviour and react to that, especially as a lot of "bad behaviour" is a sign that the child has lost control and isn't really choosing as such to do what they are doing.
So the limit might be - you're allowed to be angry but I won't let you hurt me/your sister. You can use X thing but only under certain parameters (with removal of the thing if they can't abide by these rules).
When they are little it's much easier and more effective to prevent them crossing the limit as soon as you see them hit it and put measures in place to prevent/reduce it in the future. You have to be consistent about where the line is and this can't change arbitrarily - you can't ignore something one day and go hardline on it the next for example. But you don't necessarily have to enforce things in the same way all the time as long as that limit is consistent. When they are repeatedly prevented from crossing a line eventually they understand that the line is there and they don't think about crossing it.
With this approach it's also a good idea to talk about how we deal with situations, give them alternative options, think about what you don't want and turn that around to find the positive opposite behaviour that you do want, consider whether it's a reasonable expectation (e.g. expecting a 3 year old to never raise their voice - unreasonable. Asking them not to use certain words directed at people - reasonable), if it isn't reasonable, reassess. If it is reasonable, then think OK, why aren't they doing this [positive behaviour expectation] at the moment? Can you do anything to make it easier or more pleasant for them to choose the acceptable alternative or the positive behaviour? Are they able to comprehend why one option might be preferable? Are they in control at the moment this behaviour occurs and is there anything you can do earlier on in the interaction to prevent the loss of control while still keeping the limit in place (which is the most important thing - if you find yourself constantly battling limits vs compassion it may be an idea to check whether all of your limits are really battles worth fighting right now or whether they might be something that is grown out of.)
I did (do) find it helpful to have a generic punishment up my sleeve for moments when I'm too frazzled/angry/tired/short on time to figure out something better, and it's the only thing I found which sets the limit on rudeness, since you can't physically prevent that. Violence you can remove them, the victim or yourself or pre-empt by offering an alternative non-human item to bite or hit or kick. Rudeness you cannot stop them shouting through a closed door and until they can write there's not really much they can do to express this in an acceptable way. So removal of screen time for this. It's a good idea to have it be something that you can enforce without a physical battle - I used to remove the batteries from the remote, now I hold access to all chargers, and he has to ask to charge things in the first place which can of course be revoked.
Negotiation - has its place. But never ever ever ever ever negotiate past the limit. That is so important. Try to approach every issue which is important enough to have a set limit the same way you approach car safety - you might bribe them to get into the car seat, distract with a toy, use force, encourage independence by letting them climb up themselves, explain the reasoning, even let them have a choice between one car seat or another, just sit there with the engine off until they get in, any number of tactics but the one thing you would never do is say "Oh go on then, just for today, we're not going far."