I agree with Mooshi on how to correct or try to correct the situation.

I am NOT an authority on dogs. You may want to contact a professional dog trainer for some advice.

I see my dog, while at the dog park, and once I start petting other dogs, my dog comes running over, then other dogs begin to do the same, if I have taken the time to pet them too. Sometimes one dog latches on to me for some odd reason and claims me as their's. Prue, my dog, tries to face her way into my hands, to avoid having another dog have my touch. Prue is sweet about it, so it isn't a big deal. I have only one dog.

I can see that if your situation keeps up, it may end up escalating to the point of permanent behavior.

Do you own these dogs by yourself? If there are two of you, maybe you could both be with the dogs at the same time - one on one - and then switch off from event to event.

I really would consider contacting a good, professional dog trainer. I am sure they have seen this behavior before. It sounds like something that would happen more often than not.

Good luck and keep us posted.