If your puppy was treated that way when it was 7 months, that might be why it is treating dogs that cower this way. You should have never allowed your puppy to be bullied this way.
Having two dogs to one person off lead in a dog park in my opinion should be banned. Most people cannot handle one attacking dog well, and two is beyond the scope of most people. Some people have stable dogs and do manage them ok. But if your dogs are not stable and are harrassing dogs, then the dog park is not where you belong especially with two of them.
Socializing your dog is exposing your dog to a variety of persons, places and things. It can be done totally on lead. It has NOTHING to do with letting your dog run around with a bunch of dogs off lead. That is something totally different.
Socialization for puppies is done because dogs with weaker nerves may react badly in situations that are unfamiliar. Such a dog that has had exposure to a variety of situations, with positive outcomes, will feel more confident in all situations and is unlikely to respond quickly with their ultimate defense, their teeth.
If someone does want to use dog parks, then the do need to expose their dogs to dog parks, and ensure that there dog neither bullies or is bullied, and reinforce good behavior and repeat. But this is NOT what is meant by socializing your dog.
Many dogs NEED to be socialized, but no dog NEEDs to ever set foot in a dog park. Dogs to not NEED doggy-friends -- that is anthropomorphizing dogs.
I suggest taking your dogs one at a time, and correcting your dog for any bullying behavior. It is possible that with only one at a time, your two bullying dogs will become bullied dogs. Hard to say.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC