My younger female Aussie gets along pretty well with my older Aussie/BC mix, who's a lot bigger than her (30lbs vs. 60lbs). She does try to rule the roost with him and they get mouthy with each other and rough house a lot, but they've never gotten in any serious dog fights. They steal toys from each other and she likes to bite at his legs until he's on the ground then pounce on top of him, and he tolerates everything she does very well, and dishes it back sometimes.
I was really good about socializing my older guy Tucker, he went through dog obedience class at 5 months old and part of their routine was to let the dogs off leash in the enclosure and play and socialize. So he's definitely not the issue. I haven't been so good with my younger one Krystal, who is about 6 months old, due to it being winter we haven't gotten out and about with her. Now that the weather is nicer, I've taken them to the dog park twice.
The first time, Krystal immediately started barking and growling at the other dogs as we approached the enclosure. So I put her in the small dog pen which was empty at first, and let Tucker in the big one with the "stranger danger" dogs. He immediately started to play and got along with everybody great. The female starting crying and seemed like she wanted to go in and play too. So I let her in the big enclosure and when all the other dogs came up to her she immediately got on her back and cried submissively. They all smelled her and then went about their way. She then hid under my legs and didn't really want to play right way. After about 10 minutes she found her "big brother" and started to run and play, and would go belly-up again every time one of the other dogs approached her.
Well, second time at the dog park, she did the belly-up routine, but when one particular dog would walk away after sniffing her, she would get up and run after him yelping, whining, and growling with her upper teeth bared and biting at his sides and back legs. He'd run away, and she'd chase him like this. I came over and stepped between her and him and told her "NO", and then she'd stop and seek out her Tucker and play with him. But every time this other dog came back up to her, she did the same routine, belly-up then when he walked away she went after him.
Is this aggressive behaviour, or insecurity on her part? Or insecure/aggression? What should I do to nip this in the bud? I'd really like her to be social with other dogs besides Tucker, and I don't want to be banned from the dog park!