This must be really distressing for you, your child and I don't doubt it, for your childminder too. Nobody sets out with the intent of inflicting or having any involvement in such an awful event.
Do you have a copy of your childminder's policies regarding accidents and incidents or/and access to animals?
What is the process documented for when a situation such as this arises?
Has childminder followed the process?
Have you been asked to countersign a completed accident/incident form?
What did childminder say would happen next?
Has this happened?
If you are unsatisfied which sounds like it is the case here, get your doctor's report on the injuries and photos taken at the time by childminder/you and contact the organisation that registers and regulates childminders in your area. Report the incident and what has happened in terms of actions by childminder since.
If you have lost faith in the childcare setting, you may wish to include a pet free childcare setting in your search for alternative care.
Many years ago my puppy was in his crate in my utility room. A friend went in and having been told that he was wary of strangers, put her hand into the cage to pet him. He bit her fingertip and shocked us all. She was a adult and had been advised to leave him be but did not. He did not bite again for a further three years but at that point he bit my 5 year old three times in one week. I too am a childminder and was unprepared to risk anyone else being bitten, especially a minded child. He (the dog) was rehomed to a couple with no children and has thrived since. No biting, no territorial behaviour. Just a chilled out dog. A vet told me that the overstimulation/noise etc may have contributed to him turning alpha on us.
I really hope you get this sorted to your satisfaction. It may or may not involve changing your childcare