Always saddens me to hear about a death of a kitten. It is never easy and always filled with lots of emotion. Profound sadness, second guessing on what we should of, could of...
It's okay for every one to cry and mourn the loss of innocent little kitten. It's normal.
As for the kitten, it may have had some fatal issues. Having allergy so bad to have a hematoma on the ear to needing steroids is very serious. Steroids are very hard on the liver and certain ones have been known to cause cats to permanently become diabetic (from a single steroid shot).
Even if the vet was more experienced, kitten most likely would not have survived. You can't administer steroids so routinely. It is very serious.
Eating of cat litter is also a very serious problem especially if the litter is the clumping clay kind. Next time you decide to have a kitten to brighten up you life, I would highly recommend using wheat scoop brand of litter. It is wheat based so that the kittens/cats can pass it through their body. It's also non-toxic and eco friendly.
I belong to a cat rescue group and we have had our share of kittens not surviving. Combined with our years of experience, vets who specializes in cats, and we still can't cure all the kittens and we still are left in the dark as to why a kitten didn't get better.
My heart goes out to you, your family and especially to your daughter. No one is at fault.
Sincerely,
smilingcat