I'm dog-friendly dog-lover old chap, but as much as I love to see a well-educated dog, I can fully understand people who fear them, and bad behaviours inducted by poor owners.
Is there anything you can do without annoying the neighborhood? If you think about enforcing the law and/or asking the community or condo/neighborhood board of owners/users, forget about it. You'll get nowhere past a few disapproving stares (at best) and some vehement rejection (or worse). You're one against a full bunch of people who enjoy what they're doing. They'll probably win and you'll be blacklisted.
Is there something different you can do without annoying the neighborhood? I think so. I've had to deal with family members or acquaintances whose fear of dogs was out of this world. This, you can't easily wipe it out. And it would require time you and they don't have. What you could do, is explain your fears and count on their parental sense of responsability. They have kids, as you do. They can understand what you both feel. They would also protect their kids and help them overcome their fears. You ask for their help as a community and as parents, you don't start and fight them with rules to enforce. You don't ask them not to do, which is usually the best way to upset the whole neighborhood. You ask them for help.
Starting this way, you'll not make any ennemy. In my case, what I've done was to set up some "dog-free" areas and time. So that the dogs would still be free to do things, walk, run and train. And, at the same time, they would do it far from the scared persons. It was either dog-time (20%) or human-being-time (80%). And that's what I'll recommend here. First, talk to a couple of parents. Explain the problem, focusing on your kids. Don't say what you think of dogs (consider them dangerous and dirty), don't blame the owners or the dogs, unless you want to ruin every future move. Say what you'd love to be able to do: share space and time. And carefully explain why: my kids and I are scared and I need to help them. I need to figure out a way to walk down the park with them feeling safe. How could we achieve that? Could you eventually help?
It has to look like small talk with neighbours. Then let the word spread around (because dog owners often talk when they meet, and any dog-related topic will rise) and wait a little to see if there's any improvement.
Work around a solution that involves a small area that would be dog-free at specific times, or a schedule where dogs would have to be under leash. Like: every day, from 05:00 PM to 06:00 PM : no dogs in the upper left corner of the park. Or dogs can be unleashed only after 08:00 PM. Anything that would give each side some freedom and safety. I'm still doing that when I want to "break the rules" in our park. I go when no one's around but other dog owners who walk or train their dog. Never do that with kids around. Never do that when people you don't know picnic. Respect goes both ways, but they'll never understand or have a chance to help/comply if you don't communicate with them. Be as diplomatic as possible when you explain your needs, and why you'd like to share time and space.
If there's a board of neighbours, with a monthly/quarterly meeting, it would be good to take the opportunity to explain. No accusatory tone.
From your comments, it seems like you don't know how to approach some dog owners and need a conversation trigger. I would just stop by two/three of them sitting on a bench and/or talking while watching the kids/dogs play, and ask a simple question like: "Hi folks, I see that some kids and free dogs are playing around. My children and I are really afraid of dogs, do you know of any place around this park/neighborhood where we could go? Is this place always crowded with dogs running freely? Any better time to walk around here? We're new here so we're kind of lost."
You don't blame them for their dogs or attitude. You give them an information about your family and ask for help/information. And you'll have to adjust your words to their answer, you're walking on eggs and don't want to upset a whole bunch of people.