Don't take her to the dog park again. Many dogs are not well suited to dog parks. They are uncontrolled and sometimes dangerous environments, and not meant for dogs that don't have excellent manners with other dogs.
And like LilasMom said, aggression towards other dogs is totally separate from aggression towards people. But, as with all dogs, you should always be in the room when the dog is interacting with the child. Children that young often behave inappropriately with animals. Don't allow the child to "play rough" with the dog. Encourage gentle, low-key contact, and no shouting or running.
The anxiety is something you need to start working on ASAP. Like LilasMom said, you need a professional (a behaviorist that uses positive methods, not just a trainer) to help you. You can learn a lot online by reading up on why dogs get anxious, and what makes it worse. But the bottom line is that a behaviorist is going to help you more than anyone online could.