I think the whole situation kinda stinks. I would be highly upset with my dog if it did something like that. I don't know if its normal behavior. I have 4 dogs and none of them would ever kill a kitten, especially viciously. I would venture to say that you might as well kiss the electric fence good bye, because now she knows she can get them and she will, even if that means going through the fence if she wants the cat bad enough. I'm sure you don't want her to get hit by car.
Misty- Samoyed Mix, Tannor- Golden Retriever CGC
Robyn- GSD CGC, TC, Midnite-GSD CGC,TC, Brennan-Golden Retriever CGC, Batman-Husky/Greyhound , Apollo-GSD