You are doing it right, at a park in a neutral location. You probably don't need to do it twice though, but if it isn't a hassle to you then go for it.
Have little dog treats to give them as rewards when they meet the first few times so that they have that positive trained memory of enjoying the time.
My relatives always bring their dogs when they visit, and mine is mellow, but can get territorial as well if it's a new animal she hasn't met before. So just pay attention to your dog's routines, if she gets territorial with your children at all, those are cues on how she may react to this other dog. For instance, at night she likes to lay by our feet while we visit, so if another dog challenges that, she won't like it.
She will share her bowl of food/water with some dogs, but not others. Just be on the watch out for feeding times. We put my dog's bowls on one side of the kitchen and the other dogs bowls on the other side, and feed them at the same time so they are both busy eating.
Chances are though, they are going to be great buddies and will get along pretty well.