I've not read anything other than the OP.
muy response -
i love dogs, adore them, my DD1 is terrified of them.
I've tried, hard to not let her be scared. My brother has a dog, my childmi=nder for DD2 has a dog. I pet them, play with them in fron of her, talk to her about how kind X's dog is, how he likes to kiss, his nose is wet and tickles. We have dog books, I bought dog DVds, DVds with dogs in thema nd about them. Everything I can thing of and all done in a gentle way, so it;'s always me petting the dog, never forced her near one etc
The outcome is that she loves them, from afar. If one comes near her she is utterly terrified.
So if your dog ran up to her in apark and she was terrified I'd be upset that he wasn't being conftroled in some way.
A park is a public place and therefore open to children and dogs. We both have to be responsible for our own.
You shouldn't have to get to the point where the child is terrified and then the dog is called away., Most children and many a adult don't enjoy a dog running up to them, esp these days with so many horrific incidents involving dogs and humans hitting the headlines.
Your dogs may not be dangerous, they may be wonderful dogs, but a stranger and esp a child out in apark, doesn't know that. So have a heart and stop taking the fact that some kids /adults don't like / are scared of dogs, so personally.