Why do you assume that she whines because she wants to go to the park? From your description, it sounds like she's fearful and anxious when she is at the park. Whining, like a lot of noises dogs make, can have a lot of meanings, but whatever the goal of the whining, it nearly always indicates a level of anxiety/anticipation. Sometimes it's anticipation of a good thing (one of my girls starts to whine if I don't release her to eat her food after I've put it down as quickly as she'd like), and sometimes it's anticipation of a bad thing (some dogs whine when their owners put on their shoes and grab their coat because they know it means they are leaving). Either way, it signals the dog knows something will happen next and it's causing them anxiety.
In your case, when you take your husky to the park, she shows lots of signs of anxiety and distress. She avoids other dogs, whines (anticipating other dogs will approach anyway), and shows she clearly doesn't want to be approached (baring teeth, snapping, etc). Stop taking her to the park. It's not safe for her or the other dogs there, and it's not helping her overcome her fears. Dog parks are terrible for socialization because you have so little control over the environment, and they're overwhelming for a fearful dog. If you want your dog to become comfortable around other dogs, you have to work to ensure that all her interactions are good ones; the caveat is that your dog has to be the one to decide the interactions are good. You may think it's a good experience when a friendly dog approaches her because you know there's nothing to worry about, but if she is whining, growling, or snapping, your dog clearly does not agree. She is still afraid, and she isn't having a good experience with that dog.
Instead, you want to teach her that other dogs mean good things. Try the Watch the World game with her. You want her to change how she perceives the appearance of other dogs. She may never be a dog park dog, and that's alright. Dog parks are often a risky choice for exercise anyway, because so many dogs who go are understimulated, overexcited and out of their owner's control. Instead, when your husky is ready, try introducing her to friendly dogs one on one. If she takes to them, arrange private play time where she can be comfortable and not overwhelmed by the energy and activity at the park.