I would not let him be around that little girl with the way he was behaving! That was very scary the aggression he showed to her. I know he's just a little tiny dog but would that be appropriate behavior for a large dog? Absolutely not~
You need to consult and expert who can deal with his behavior before he bites someone. I do think when he was being held back from the little girl it made his behavior even worse. Until you can get him into some training classes with a behaviorist I would suggest that he be crated while your are babysitting or workers are in the house. Both for his safety and others.