Well, in MY industry, we also go back and review things and go over procedures and attempt to learn from experiences.
But my industry- hahahaha- is cat poop and cats
Look-- the only thing at this point I'd look at is your experience with the vet and at the vet. Is inducing vomiting the right response to this situation? I don't know, but I do know at least one of your vets (assuming you were using an emergency vet and a regular vet) was excellent and your girl is alive today because of great medical care.
If you are iffy on the recommendation to induce vomiting, ask yourself this-- do you have other e-vet choices (assuming it was the e-vet that gave you the recommendation)? If so, than you might look into using a different one. Another thing to add to this entire thing is-- although breeders are NOT vets-- this is where having an involved breeder can be a very positive thing too. Call them and bounce ideas/diagnosis/recommendations off of them. While using the forum is top-notch, it can be a bit confusing too because often, you will get many many different opinions (hahaha-- as in the feeding topic-- so many opinions!) so having a good breeder you can trust with a great vet usually makes a very nice safety net for kitten owners (that's just a random PSA.)