Sorry Mel, they are right. It is cruel and has been proven to be so. Its definately one of the cruelest ways you can kill a rodent, live feeding even kills them quicker. It is far from painless freezing a mammal to death.
If you don't want to whack them in front of your daughter..don't do it in front of your daughter.
If you can't stomach it, do what we've been doing for years and buy them frozen prepacked (we use pythoninfinite, the best rats around).
We used to breed rats and mice years ago, I used cervical dislocation or whacking method. It was hard and I don't think I could do it again, which is why we buy frozen now, even though it probably costs more. But we buy hundreds of them in bulk, about 6 months worth and it's much better.
Hope it helps, like Baz said google it and you will find it is most definatley painful. Hopefully you can find another method and save further pain to your feeders.