In order to assess whether your dog is enjoying her day at the park or not it is important to be able to read her body language. Here are a few of the more common social signals (body language) for which to look:
*) Tail tucked between the legs shows fear
*) Hackles up (hair the neck, shoulders, down the spin, or at the root of the tail) indicates arousal and probably fear
*) Play should be balanced. If your dog is always on the bottom it is unlikely he is having fun
*) Show of eye whites
*) Stiffness, standing very erect, tail held high; these are displays that may indicate the dog lacks confidence in that situation and is deciding what to do next.
Don't under estimate how much your dog needs you to protect her and make safe decisions for her. Don't forget that you got your dog to be your buddy. You didn't get her for all the dogs in the dog park. Your dog should play with you. And that is the short answer.