I have two little boys, they will be 4 and 5 in a few weeks. I cannot leave them around my Guinnie without me EVER. My oldest is usually the more mild one, but he had a huge issue with Guinness and his teething, so I know to not let him around him without me there.  My youngest is much more gentle but they both like to run with Guinness and have him chase them, I worry so badly they will hurt him. So, I limit the time and make sure they know to sit still and pet Guinnie and not run, we are learning how to play tug of war with him.
 
It's constant. 
I'm glad your puppy is okay and I think a sterm talk with your daughter will help, but you will probably have to constantly remind her. I use the word 'gentle' over and over with my boys. 
(((hugs))) I'm sure you got a big scare with that