I expect the reason the dragon bit your daughter is because she was dragging him out from underneath a dresser by his tail. It was defending itself from what it felt was an attack.
Having a puppy around doesn't make things easy for your dragon either. Even if the doesn't have visual contact he can still hear and smell it. I am also sure your daughter pets and holds your puppy often, so its scent would be all over her too.
Just explain to your daughter the dragon didn't bite her out of meanness...it was scared when she grabbed its tail, she probably hurt it too. So he did the only thing it could, and bit. Dragon's can't say 'ouch'. To your dragon, your daughter attacked it...he is acting aggressively now because he was hurt by 'people' so you will have to reestablish the whole trust thing again.
I don't go with the grab him and hold him no matter what practice of gaining an animal's trust. This is far to stressful for them. Not to mention there is too much chance of injury to the person and lizard. If gloves are worn then its even easier to cause injury to the dragon.
Best thing to do is just leave him alone for a week or two...make no attempts to hold him etc. When doing anything in his cage (cleaning, feeding etc) keep your movements slow and as away from him as possible. Move hands into the cage for his level or lower, instead of from above. If you are really worried he will lunge at you, place a cardboard barrier between you and the dragon till you are done spot cleaning etc. then remove it from the cage.
After about a week or two, offer his favorite treats by hand, talking calmly to it. Slowly establish trust again. Once he stops flaring up when you are hand feeding it etc, carefully pick him up and make sure his feet is well supported. He may struggle but be calm and gentle. As soon as he calms down put him back into the cage. Increase time out longer over a few weeks.
I also advise washing your hands if you have been petting the dog before doing anything around your dragon.
Once the dragon calm in hand again, you can get him used to your daughter too and she as well.
Keep in mind all animals can bite but none will bite out of spite or meanness. They bite accidentally (in play) or because they are frightened or defending themselves or territory. Even human kids go through a phase of biting.
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PHLdyPayne