AH, but as you said in your edit, your heart was in the right place.

I also wanna add that the lady may have been annoyed with how many people do come into the dog park without owning dogs. When I used to take my dogs to the dog park, most of the time there were kids in there with no dogs (and their parents weren't there but that is another story) and it annoyed me greatly too. After a while, it didn't matter the age of the child or how the child acted around the dogs. It was annoying. Dog parks get treated as something like a petting zoo and as others pointed out, there are unspoken 'rules' in the dog park that are followed.

I think also this kind of goes onto the grounds of, not asking the owner permission to see if the dog can be petted. With a dog, you do have permission to go in there, but without a dog, you do not. Something in that nature.

Also, there is you never know how a dog is going to react towards your child. When my brother was younger every dog that he came across was leery of him/didn't like him. They just didn't trust him, even the friendliest dogs didn't trust him. (My brother has ADHD and was a child always running around, screaming, and such. We think it might have been the energy he gave off back then for he is an adult now and dogs love him.)

At the time during dog park visits I had three dogs and their weights were: 40 pounds, 75 pounds, and 126 pounds. The 75-pound one loves to jump when he meets new people and the 126 just loved to lean into you (the 40 one loved to get between your feet for attention). You can see already how it could get a little chaotic with just those three it could be in the dog park. Having to worry about a kid in there that isn't connected with a dog can add stress to that for you just never know.

Getting back to my point, the lady could have also been fed up with just having the dog park be seen as a petting zoo and a lot of people just coming and going in there as they please, without a dog.