R.W.
Yikes! This is extremely dangerous!! Dogs can respond unexpectedly. Obviously, you don't want the dogs hurt, and the fact that she may be deliberately trying to hurt the dogs is disturbing, and will need to be dealt with...but what really concerns me is that any dog may attack her- instinctively- because of her behavior. If this is a pattern she has developed, and she does it with different dogs, imagine if she approaches a dog in the park or any dog she sees, and does this...I'm sorry to point this out, but a young child can be hurt, traumatized, mutilated, even killed by a dog, with little provocation. Large dogs, nervous dogs, mistrustful dogs, dogs with sore body parts, dogs with dominance confusion, dogs with aggression inbred...even family dogs with no history of aggression can suddenly and very quickly turn on a child and bite them in the face. (I know of two family dogs that were put down because of this.)
The fact that your 3 year old is able to "pin" your dog suggests that this is a pretty small dog you have in your home, but it's still a bad situation, and a very dangerous habit. You should discuss this with your veterinarian! And probably your pediatrician.