Here's what I'd do if she was my dog. I'd stop playing into her fears and trying to force the issue immediately.

Then I'd take her on the prong collar and a good solid leash to an area where there are children playing. I'd find a comfortable spot far away from the children but close enough that she can see and hear them. Even as far as a half block away would work in the beginning. Far enough away that she shows no reaction to their presence. Then sit down and relax with her in a completely normal manner. Sit back and read a book if you want to. Do this every day until she comes to take the presence of the children, their fast moves and noises completely for granted. If any children approach during this time politely wave them away and tell them she's in training.

As she becomes more desensatized move in a little closer every few days until she is comfortable within a few yards of the playground. This could take anywhere from 2 weeks to six months depending on the extent of her fears.

Once she has reached the point where she ignores the children completely, then and only then would be the time to gradually introduce the children you want her to meet.

Do it in the same way, by having them play at a comfortable distance for several days and gradually moving closer while talking to you from a distance. Only when she shows no reaction or simply shows normal interest would be the time to let them come close enough to hold out their hand for her to smell. By the time she's gotten to that point, she should be just fine with them within a few more days.

Good luck!