Thank you for posting this thread!! I've recently started taking Hudson to the dog park too so it's nice to see other yorkie owners being considerate about asking what appropriate etiquette is.
Hudson plays nice with all the dogs but when I first started taking him I watched him like a hawk. Just because you don't know what the other dogs and dog owners are like and how your dog will interact with all the others. Hudson hasn't been neutered yet (his appt is later this month) and the other day he hopped on top of another dog and started humping. I was a little mortified but luckily the other dog's owner just laughed it off. You never know though, so I always like to be careful.
One other thing that happened to me recently was that a mother had brought her dog and her two little girls. One of the girls (probably 7 yrs old?) asked me if she could play with Hudson and when I said yes she picked him up and walked him over to the other side of the park. I was a little surprised but I can understand (he's so darn cute and little!!). At first I didn't mind, however, she did this a number of times and I had to watch her to make sure she was holding him correctly. She was taking him to the other side of the park where I couldn't see him as well and putting him on a bench. I know she just wanted to play with him all by herself but after awhile I asked her to not pick him anymore so that Hudson "could play with the other dogs and get exercise." She did it again one more time until her mother had to intervene.
Just thought I'd share my story in case anyone else has had interesting dog park stories to share!