To be fair, your question wasn't answered. If I were you, this is what I would work on. 1. Handler focus. There are lots of ways to do this and you should include it in all parts of training if you can whether brief or sustained. This includes eye contact, attention/redirection towards you when you say her name. Work on eye contact/attention during meals. Work on some duration. Ask/test her response when she is distracted like around the house playing with the other dog, barking at a distraction, focused on a chew, playing with other members in the house. This will give you an idea which areas she struggles in. 2. Recall. On top of the response to name, work on the recall a lot. Because she will already have a history of giving you attention when her name is being called, introduce a recall cue. I like to say their name and then the recall command. To me, the name grabs their attention and then gets them ready for the next command. Kind of like when someone says your name and your response would be "what?". Do this off leash at home and on leash in easy areas. Do this on walks and don't forget to use leash pressure appropriately as additional guidance. Play lots of recall games. Some games include paper plate recall, restrained recall, hide and seek, etc. I don't know what motivates your dog. I remember that your dog is not really motivated by food, but for easy obedience start rewarding with her kibble so she gets in the habit of accepting that as a reward also. I'm sure you know how the reward system works so do what works, but try to introduce other forms of rewards too like small personal play, petting, food, toys (whatever you use and what will work will depend on a lot of things). 3. Stay. Work on this. Work around distractions such as around other dogs. If you can, try to get some eye contact out of her. In order to train her to ignore/be stoic around other dogs without having to train in an environment full of loose dogs, you will have to work on your engagement with her. For example, in the video at the dog park I can see that even though she's not watching you, she is clearly paying attention to you (see the flicking of the left ear). Those are the moments when you want to train and reward her for any attention towards you. Be an active part of the reward. That way instead of being so focused and then defensive when other dogs come around, you are redirecting her attention and teaching her to ignore the other dogs and engage with you. 4. Integrate all her skills. If you can, teach an emergency stop/freeze command.
Also, you should carry some sort of self defense item that will help you defend your dog against loose dogs. Put your dog in a stay and get in front of her and do whatever you can to get the dog to leave. You must prove to her that you are capable of keeping her safe from other dogs. Start doing this at the dog park if you continue to go. Work on obedience, but when you see dogs coming towards her, you need to make sure that YOU are the one to make them leave, not her. She should only worry about what she's being told to do and trust you to take care of the rest.
She will gain confidence as she gets older and the bond you two build through obedience drills, everyday activities will all help her learn to look to you for direction. Do lots of obedience and walks outside of the perimeter of the dog park. Obedience needs to be solid, but it needs to be more solid around innocent people.
Like you said, flight responses took over and I think her guardian instincts kicked in when she saw how close that man was to you. I think her reaction would have been different if the dog had came after you.
