Hi there!
I'd love to get more into this conversation, but I have little time so my input will be limited.
About the 1st photo you posted: I don't feel that there is too much negative space there, but I do not like the poition of the cat. It seems to weigh that area of the portrait, and is distracting the way it is cropped. But, I could see this one working just fine without the cat, if she just had her arms relaxed and meeting in front of her off the picture plane.
The 2nd picture is almost there, I'd just add a little more space so that the cat isn't cut off. Then, the cat will be better balanced by your daughter, and you will have pleasing negative space on the top and bottom of the picture. See Chris Saper's "Cotton's Kid" to get an idea of what I mean.
Lovely model, I love the green color, can't wait to see the portrait, I hope to get back to or at least read more of this thread later!