children hurting kittens

We have seven years old daughter and a cat, who recently has kittens. Our daughter does love the cats passionately, but - of course - cannot handle them the way they would like to be handled. She often wants to have a cat in her arms, when the cat doesn’t want to and she catches them again and again when they try to run away. The adult cat would scratch or bite, when she is not happy with the treatment, but the kittens cannot do it strongly enough - they just cry - and our daughter continues to try to make them stay with her until we ask her to let the cat be. But if we ask her to let the cat be, it would start an issue between us, because she - of course - hates to be corrected. 

We have tried to say nothing , when the cats are not happy with her treatment, but then she treated them more and more disrespectful. She also likes to clean their eyes and noses and nails against their will and, because she knows that I don’t like it, she usually takes the cat outside and does it to her, or turns back to me, so that I cannot see it. I don’t know what to do, I can see that she cannot help herself not to do that but I don’t want the animals in our house to be unhappy... She even often tells me a story about a mummy, a little girl and a cat. In this story the little girl is an evil, who doesn’t like the cat and hurts her and the mommy is the good one who always protects the cat. Ones i told her that I feel said for the girl, because her mom is so disrespectful of her needs, and cares much more of the cat, but my daughter in this story really loves the mom and the cat and hates the little girl and wants her to be hurt...

Do you think, that it is possible to have free little children and happy animals in one house?