I think the best thing to do is model empathic behavior in front of her. So, when she screams in Finn's face and he's visibly upset, comfort Finn and talk out loud to him about how that looked like it scared him and that's not fun and he didn't seem to like it. Focus on Finn to Finn about how he feels rather than telling Nora what she did wrong. KWIM? Take care of someone who is sick in front of her so she sees what is nice and appropriate. Maybe give her things she can do to help you when you are sick. If she wants to jump on your back when you aren't feeling well, maybe she'd accept rubbing your back. Kellen likes to rub my back and Ethan likes to brush my hair.
The last thing that comes to mind is to show her empathy every chance you get. I absolutely hate it when I see a small child get hurt and is crying and the parent just tells the child that he is all right and to get up and brush it off. The child may not need to go to the ER but he is obviously not all right or he wouldn't be crying. So, instead of telling the child that he's all right, express your understanding of their hurt, kiss it, hug the child, comfort him. People seem to think that doing that will cause the child to cry over everything and by a "cry baby". My experience has been the opposite. The more responsive I am to their feelings the faster they get over being hurt and the less often they cry over the smallest bumps.
I think if a child hits once, that can be dealt with quickly, once. Ideally, the person who got hit would express his pain in a reasonable way and make it clear that he doesn't want to be the child if she's going to hit. If the child continually hits, then I think it's appropriate to remove the child from the situation. If the child hits, the child can't be around other people. That's not quite the same as a time out. With a time out, you have a preset time limit, usually one minute for each year the child is old, during which the child has to stay in a specific place. I doubt that Nora would learn much about her behavior by having to sit somewhere by herself for 4 minutes. It's much better for an adult to gently remove her from the situation and explain that you will not allow her to hurt other people. If that means she can't be around other people, than that is how it will be.
Why did she lash out like that? Was she angry or scared? Was everyone ganging up on her trying to get her to stop whatever she was doing or to fix what she had done? If she was angry, talking to her about and showing her other ways to express her anger are important. But it won't do any good if the other adults don't allow her to express her anger in a healthy way. If she was scared, that needs to be addressed with the other adults. They need to understand what they did that scared her and how they can do things differently in the future.
It probably would have gone a long way if someone had helped her put the decorations back. I don't think that I'd expect a 4 year old to know how to do that quite right. Maybe she didn't know exactly where the decorations were supposed to go and how. Maybe she needed more guidance. Grandma could have looked at each decoration with Nora and then shown her where and/or how to put it back.
I think that other people have the right to have different rules in their homes but I don't think they have the right to use different, especially harsher, discipline tactics than the parent does. Honestly, if the grandparents can't respect the way you discipline and do things your way with your children, then they probably shouldn't be watching the children, at least not for extended periods. Yeah, that can make things a little harder for the parents but it's only for a short time. Pretty soon the child will be old enough to behave differently and before you know the child will be old enough to be left alone.