How do you suggest dealing with things such as calling me names (like dumb and stupid), throwing things at me or other members of the family, destroying something in the house or other such behavior?
How do I be sensitive to my child's needs and yet still teach her about boundaries?
I'd read those kinds of outbursts as signal flares or indicators that tell you your child's nervous system is overwhelmed. When she's feeling calm and centered, those things don't happen. And once she's already gone over the edge, she's no longer receptive to reason or a lesson.
This is why parents are so often frustrated that their kids continue to repeat undesirable behaviors even after they've given them a consequence. Children who are focusing on their own pain, loss, or disappointment are not receptive to learning. Additionally, consequences alone do not teach children what you want them to do next time. They need concrete guidance during a time when their brains are receptive to learning in order to make a change.
So, what's a parent to do? First, intervene to insure safety. Gently contain your child and/or move the victim or object out of reach.
Then tell her it looks like she's feeling overwhelmed, and that you will help her. She needs your assistance with learning how to read her own cues. Saying things like, "Uh-oh, when I see you starting to push I know it means you need some space. Let me help you find some," lays the groundwork for her to interpret her internal cues by herself.
Eventually she will be able to initiate protective action on her own. Every time you read and respond to her behavior as communication, you help her learn more about her temperament and her needs, and how to advocate for them in healthy and appropriate ways.
Give her the language you want her to use by saying to the other party, "Susie is needing some space right now, so she's going to play over here on her own for a little while. Please don't go near her. When she's feeling ready to play with you again, she will come and find you."
Hopefully, children are very physically attuned to their adult caregivers, and take great comfort from their presence. So the closer you can keep her to you when she's overwhelmed or stressed out, the sooner she can entrain to your calmness and settle down. You may want to invite her sit on the kitchen floor and color while you are cooking or whatever. It doesn't mean you have to drop everything and focus on her. Just let her be close.
To recap so far: your first job is always to insure safety. Then to help her settle down (and remember to settle yourself down, too!) Emotional upset and learning do not mix, so there's no point in trying to reason with or instruct or correct an overwhelmed child. Only after she is feeling safe, calmer, and connected to you again does the teachable moment become possible.
So later that day, when she's relaxed and open, that's when you say, "Hey, let's talk about what is going on for you when you start pushing (namecalling, throwing, etc). I'm wondering if that's your way of saying (I need a break, I'm really frustrated, I'm sad that I can't have what I want, I'm tired, I'm angry, etc). And the thing is, it's hard for me and others to listen to messages that hurt or scare us, so let's see if we can figure out a way for you to tell us what's going on for you in a way that we can hear it better."
Listen to her suggestions, and decide together on a phrase or gesture that she can use to signal to you that internal pressure or frustration is building up and she's gonna blow. Do your best to respond right away when she gives you the signal - her fuse is probably very short at this point in time, and she's still learning, so there might be only a very small window to intervene before she takes matters into her own hands.
I hope this helps. If you'd like help working through this process, I'm available for parenting consultations by phone and email. Please feel free to contact me at firstname.lastname@example.org .