I find this difference in behavior based on the number of dogs present at the dog park fascinating. I could only make guesses as to why it would make such a marked difference regarding the dog's behavior. Maybe something along the lines of security/comfort/strength in numbers??? I sure don't know. Hopefully, some of the forum members who are educated in this particular sector of dog behavior would be willing to share their thoughts.
This is what is interesting me the most in this behavior, as well.
My thought, and this is a wild stab in the dark, given that I've not seen the behavior and am working on limited description. My thought is that with more dogs, maybe he's overwhelmed enough that he won't react aggressively, and perhaps the emotional discomfort he is experiencing is presenting as "silliness"/"excitement" instead, since he feels aggression is not a valid behavioral option in a large group of dogs but is still very stressed.
Alternatively, it could be that he feels that large numbers of dogs is safer than smaller numbers- has he ever had any uncomfortable situations with smaller numbers of dogs, perhaps?
It is also possible that he is just exhibiting extreme barrier frustration on the leash, but I would expect that to translate to fences were that the case (given the described severity on the leash) and wouldn't expect there to be a difference between more or less dogs in the dog park.
A few questions about the dog: what is he like- fearful/insecure, confident, friendly to people? What is his play style like with other dogs? At the park, how does he act- wrestling, chasing, just chilling out?
I have a few thoughts:
1) While I agree that owners quite often misconstrue things like frustration related aggression, a dog can still have barrier frustration and want to hurt the other dog. I hesitate to underplay the severity of any kind of aggressive behavior over the internet, personally. My biggest advice: find a professional able to help in person, locally. This forum is a wonderful place for information, but in cases of aggression people over the internet can only help so much, and there is a wide gap in reading/learning the information and actually successfully applying it. There is always a learning curve, and with a dangerously aggressive dog (which it sounds like you think your dog is, ignoring the possibility that the behavior is being misinterpreted), it isn't the time for a learning curve. Do use caution in choosing a trainer to work with- there are a lot of bad trainers out there. I'd suggest looking for some kind of credentials- having been CPDT-KA or KPA-KA assessed is a good start. If you can find someone from the IABC (International Association of Behavior Consultants) near you, then that would be great, IMO.
2) Be VERY sure that you have a secure hold on this dog on walks. Personally, my preference for dogs who I consider risky (usually meaning they have some form of aggression and/or reactivity to certain things in the world) is a front clip harness (my new preferred brand is a Sensation harness) with a flat collar, with the leash attached to the harness and the collar and harness attached by a caribeaner. I worry about dogs slipping out of collars or harnesses alone, personally, and I actually feel I have more of a hold on a dog in a front clip harness than a collar, though that is totally preference. A lot of people like head collars, but it is imperative to learn how to use them from someone who has experience with the, and they take a long time to get a dog used to most of the time. Make sure the equipment is in good shape.
2.5) A muzzle isn't a bad idea if you are truly worried this dog would seriously injure another dog if given the chance. As others said, there is a real worry of liability with an aggressive dog, should it ever bite, and a muzzle can cover your bases and take away that worry somewhat. Also, other dog owners will be more likely to stay away from a muzzled dog they see from afar.
3) I would advise avoiding other dogs as much as possible when on leash until a very clear training plan is in place (which I'll talk about below a little). When I'm working with a dog who is iffy with certain things (meaning it has any kind of strong emotional reaction to something- this is usually to other dogs, leading to things like over excitement, anxiety, fear, leading to lunging, barking, and general crazy behavior) I always teach a direction changing cue for emergency U turns. I use the phrase "this way". When working with a reactive/aggressive dog, you want to avoid the dog rehearsing the behavior as much as possible while encouraging the response you do want as much as possible. I use an emergency U-turn for things like:
- Other dog is too close and I know the dog I have will react
- I know the other dog is aggressive/reactive itself and thus that the dog I have is likely to react (it is important to note that a dog may be at a point where is can ignore or mostly ignore uninterested/neutral dogs but still freaks out at dogs that are interested in it or especially those that are aggressive themselves).
- I doubt the ability of the other handler (owner) to control their dog, or know they tend to be the type to not understand I don't want them to bring their dog over to the one I have
- I'm not set up for a training session or not up for one (meaning I either don't have any treats or toy rewards on me- usually because we were just running out for a bathroom break- or I don't have time to stop and work on the issue then and there)
You want to teach the cue away from other dogs and use it occasionally when there are no other dogs to avoid that phrase meaning "there's another dog near bye and you should be on alert". Also, try your best to calm yourself and avoid the cue meaning that for YOU. This is where a muzzle and safe equipment will help, because you'll be less anxious knowing the dog can't get to the other dog (I speak from experience).
4) For the training part of it: the goal of (good) behavioral modification (which is what this would be) is to change the underlying emotional reaction to the stimulus (in this case other dogs) and to teach an alternative, more desirable behavior to replace the ones you don't like (ie, the aggressive ones). Some people train a sit/stay with the dog watching them, some people play a game where they'll toss food for the dog to find while moving, some people ask for tricks while they move past other dogs, some train a close heel with attention. It's really all about what behavior works best for you and for the dog. My personal favorite (the one I think works best for people with pet dogs) is the "find it" game- you say "find it" and toss a treat and the dog goes and runs after it. This takes the focus off the other dog and keeps their mind occupied with something else. It will also make them more attentive to you. I usually like to change this into something else (dog doing tricks or a sit/stay) eventually, but I think it is a good start and a good first goal to be able to play this game without the dog getting distracted prior to trying to add more complex behaviors. You would have to practice this where there are no dogs until the dog is really engaged in the game, and then try it with dogs far away, moving slowly closer until the dog doesn't care about the other dogs.
Again- the best thing you can do is to get a professional to help in person, though. The above is a very brief description of a possible course of action that sounds easy, but is not going to be as easy to use as it sounds. It will take time, there will be good and bad days, but there is hope that eventually it will be manageable with long term training.