Dog park woes

Ever since their first car ride home from the greyhound haul, Betsy has always disliked Catcher (Kory's foster). She barks and snarls at him whenever he touches her. Brooke, Chomps and Mouse... she has never had a problem with them. For this reason, I've always stayed away from dog parks with her. Well, I was brave the other day and I took her and Mouse up to the Lakewood Park. Surprisingly, she did fantastic! I saw a side of her I had never seen before. She got along with all the dogs and she absolutely loved all the people. The majority of her time was spent looking for people to pet her.

So today I decided to take them up to the Avon Lake Dog Park, which has grass! Lakewood pretty much only has gravel, and greys apparently don't like to run on gravel. It also has a bunch of trees that Mouse loves to weave in and out of like it's an obstacle course. I opened up the gate to let them in, and before I could hang the leashes up, Betsy and some big white dog were a big ball of fur and teeth and snarls. We split them up and went on our ways. Betsy later got in a fight with the same dog while it was leaving. The owner said, "Does she usually do this?" I wanted to smack her, but instead I told her that Betsy will growl or bark if a dog is bothering her, never before have I seen her get in an actual fight.

I know none of this is really a big deal, but it bothers me because Betsy really seemed to enjoy herself otherwise, and now I'm very hesitant to take her again. Either way, if dogs didn't do things like in the picture below, all would be peaceful. That is a different dog btw, Betsy only snarled at him and he got the idea to stay away.