All the above!
Everything your doing with the dog is bass ackwards but, with Steve's first comment above, it sound like you may have known that already.

Well John, looks like you got the jist of it already from some very knowledgable people. I would take their advise.

@Barbara Yeah I'm sure your right Barbara, me, the cat, and maybe even the girlfriend and her dog are more than enough to make a pack. I don't see any real reason to try to expand it even more. Her getting along great with my girlfriend's dog at least shows me that she isn't dog aggressive, but I'm sure if these situations keep happening and a bad event takes place then she will be.

@Connie Yes You are right as well, especially on correcting her, I didn't feel good doing it but i simply didn't want her to think biting other dogs like that was okay. Luckily I've only corrected her for this(by mistake) for one day, so I'll stop that immediately.

@Steve You would be correct, ever since I found this site months ago I've been reading up all i could and even watched Ed's videos on puppy8weeks-8months and basic obedience and listened to several of his podcasts. But i would like to state the only times I truly stepped in between her and another dog were for those 2 aggressive ones, for the other times shes ran to me I've only done so until I noticed that the other dog wasn't being aggressive and let her go away from me when she was calm again.
And I feel the same way about trying to create a bond with the ball as a medium of sorts.

@Samantha I actually met my girlfriend in a basic puppy obedience class. So our bond with the dogs is important for both of us. And I cant believe I haven't thought of giving her treats when she sees other dogs on walks, which only happens once in a while(seeing dogs, we walk almost everyday), but that could help.

And to everyone here Thank you for all of the advice, It really is what I needed, to reassure myself that my gut feeling of not liking dog parks was right. I will try to pass this trough with my girlfriend and see if we can make some time away from the dog park for all of us.
Once again, Thanks.

 Quote: Betty Landercasp

There is "mine" and "I'll yield to a higher authority", but I don't think they really understand "share".

I see your point, and think you are correct. She does let people near me take her toys but not dogs, so I think she may understand that when I know the person it's okay. That would probably the higher authority, but you're right: sharing isn't a natural behavior for them.

I'll chime in to agree with the suggestion about finding a puppy class or beginner obedience class taught by your local training club. Invite the girlfriend and her dog to go along too.

These classes are a great way IMO to "socialize" (which, in a good class will mostly be about teaching your pup to ignore other dogs and focus on YOU instead.)

Like everyone else has said, dog parks just aren't a very good scene. Maybe you and the girlfriend and the two dogs could meet there where nobody else is there (10 pm?) and give only your two pups a chance to run off leash. But if anybody else showed up, leave.

In a big city, there have to be other places where you can go with your dog and girlfriend besides a dog park. How about a regular old park? Then your little pack can walk together and work on leash manners and ignoring other dogs. Walking together as a pack, with a good leader, is a great way to build or reinforce an appropriate dynamic for happy household pets. IMO