I think it's a mistake honestly. You told the trainer that she is dog reactive and that trainer's reaction was "My thoughts...honestly my thoughts are that she needs to be socialized." And she based this on???? "Give her a chance in a safe setting..with a muzzle until you see what she will do." A SAFE setting? There is nothing "safe" about a dog park, not for half of the dogs out there. And we all know that already.
Telling you to just throw a muzzle on your reactive dog and go through the dog park as if it's no big deal tells me that she is missing something in her experience with dog training. If it goes well, then that's great, however, if it goes badly... someone who thought that it was going to be no big deal in the first place is not going to know how to handle the problem, or ultimately fix it - and since she caused it, she should be the one to fix it.
Dock diving is fun, and free is always extra fun... but the potential for a problem is to great in my opinion.
All that said, since Ginger thinks it's ok, then go for it... since if it goes bad, Ginger will be fixing it.