Who’s at fault here?

So I’m at the dog park with my big black lab. My lab is my hunting helper so she has a high prey drive, but we have trained her around other dogs so she is very social and does well. Well we have a split park, all dogs over fifty pounds on one side and all under on the other. This way big dogs are with big dogs and little dogs are with little dogs. Our dog does great with this as she has a high prey drive and tends to get too rough with little dogs. She has never hurt a little dog, just gets rough with them. So we keep her away from them, for our sake and the other owners. Well, we are on the big side and this lady brings her glitter collar chihuahua to the big side.... immediately I call for my dog to come sit between my legs because I want to make sure she doesn’t get rough because I can tell this will not go well with this lady. I get my girl all ready to go with the leash and start heading out. I even chose to exit on the other side to avoid. Well, the little dog intercepted us leaving and starts growling and barking at my girl. Our dog starts getting excited, nipping, jumping, barking, and getting a bit rough with the play. I keep trying to leave and this little dog won’t get out of our way. Well here comes the owner screaming “oh my gosh! Oh my gosh!” Thinking my dog is attacking or something? She comes over cursing like a sailor and swings the metal end of her dogs leash at my dog. My dog yips loud and this lady starts yelling at me to control my dog and how my dog doesn’t belong there. All while here dog is still growling and barking at mine. I end up picking up my 100lb dog to get her out of the gate while the rat is barking, growling, and jumping at my dog I’m carrying and the owner is yelling at me. We get outside the gate and the owner this screaming at her husband about her baby (the dog) who is telling her to knock it off. Once in the car I just looked over my girl, she was okay, but shaking from being hit. I get that your dogs can be really important to you and you want to always protect them, but my dog was not hurting hers and hers wouldn’t go away. Mine tends to react more on the leash because she feels trapped and can’t get away. We haven’t been back in away because I don’t want that to happen again, but my girl loves it there and has friends. Was I in the wrong? Can I take my girl back?

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