Now it's my turn and eh, not so fun...

I have been watching my niece, H and D these past couple of days. H goes back to her mama this Saturday. These girls are making me want to pull my hair out!! I'm pretty sure that when they are over at my sister's, she doesn't have this problem because H shares all her toys with D. She lets D use everything and seems happy to do so because she is almost seven so she understands the art of sharing. D, on the other hand, is only 2.5 and while she has made great strides in understanding possession and not being so possessive of toys that we find out at school or at playgrounds, she is very possessive of her toys in her house. So...that makes for some very unpleasant encounters. And I don't want to always defer to H to be "the bigger/older sister" and understand. That's not very fair so I try to be reasonable for each situation.
I'm not gonna lie. The first couple of mornings involved a lot of screaming...by D and then on my part. Just so sick and tired of H trying to take something just to look at it or whatever and D screaming at the top of her lungs because she doesn't want H touching anything of hers. Ruuuuddde.
And since I am now trying very hard to understand the art of non-violent communication and communication that builds confidence in a young child, it is so very hard for me to decipher what is right and what is wrong when it comes to communicating with these two girls. Needless to say, I have been EXHAUSTED at the end of each day.
Another thing is I know H does things that she knows will irritate D. While it's not really hurting D, it does cause D to scream and then H lies that she didn't do anything. How does one deal with THAT?? Case in point, the other morning, D was walking around with her helium doggie, loving on it, etc. She didn't want H to touch Nashuan (the dog's name). I turn my head, go into the kitchen for something and then I hear D screaming and then crying. I run over there to see what is going on.
Me: What happened, D? Why are you crying?
D: H stepped on Nashuan!! (clearly you can see why this would be a upsetting to a 2 year old)
H: No, I did not. I mean, I did but it's cuz I didn't see it.
Hello, people. The dog is RIGHT THERE. There is no way she didn't see it!
I mean, my response was just that. "Come on H. There's no way you could've not seen the dog."
I felt terrible saying that, but it's true!!
Anyway, suffice it to say I am at my wit's end with this non violent communication thing. It hurts my head...