I'd pick up the balls at the dog park or not take her there at all (I know how many toys they have scattered about. My dog almost got attacked at a dog park when I took her once as a puppy over something your dog does. Some dog had a ball and my girl sniffed him and he ran her off til she was screaming. We never went back there.
I have to be careful with water because my dog likes to set up camp at a water dish when she is tired and scare off all the dogs that come close and it's inappropriate...so if we're in a situation with multiple dogs and a water dish I either keep my dog on a leash or call her away every time she walks close to the water. she can come drink from her own bowl I bring.
Find a way to prevent her from getting a ball and trying to hoard it, you guys can play ball all you want when other dogs aren't around