I like all of the suggestions already given to you. Indoor play areas, smaller parks, taking a friend, etc.
I have 2 kids, a boy age 4 and a girl age 2. My best friend has 3 kids, a girl age 5, a boy age 3, and a girl age 1. Both of us take our kids just about everywhere together and on our own without too many problems. Your kids are pretty young right now, so it's the perfect time to start teaching them safety rules and how to behave out in public.
My son has enough energy for 3 kids and he was a BOLTER from age 1.5 to 3.5. But the more I took him out and the more we practiced our family's safety rules, he eventually got it. Now I can take them both to places like the Wild Animal Park, the Zoo, the parks, the pool, the mall....pretty much anywhere on my own without worrying....as much. Our rule is everyone needs to stay where THEY can see Mommy, not the other way around. And if THEY hear Mommy/Daddy calling their name, they need to answer "I'm right here Mommy" very loud. And for each place that we go to, once we get there, I show them the boundary that they need to stay in. At the park it's usually the play area, at the amusement parks, they need to be walking within a 10 foot distance IN FRONT of me. When we go to the beach, my husband draws a huge circle around us that they must stay in. If you cross the line or don't stay in the play area the first offense is a time out. Second offense is a spanking, third offense we go home. Period, end of story. And each time we explain to them the safety rules and why we have them. My son understands that he needs to stay in the safety area so that he doesn't get lost, so that a stranger can't take him from us, or so that his baby sister doesn't get lost or taken while Mommy is out looking for him.
Don't get me wrong, my son usually ends up in time out and we periodically have to go home because he is a repeat offender of the safety rules, but I know he understands the rules. I know this because when he goes out with my best friend, or other people who will occasionally take care of him, he follows our family safety rules with them and will even tell them what they are. And if he sees his sister straying, which isn't often, he will go and find her and tell her the safety rules.
I am not sure how old your daughter is, but I will often ask my son to "help" me watch his younger sister. It boosts his ego and makes him feel important. It only lasts for a few minutes at a time, but he will sort of keep an eye on her while he plays. So maybe you can have your daughter "help" you by making sure her younger siblings don't put stuff in their mouth. That will make her feel good, plus it will force her to stay close by to "watch the babies".
I would also suggest maybe starting off with shorter time periods at the park...at least until you feel more comfortable doing it. Maybe 30-40 minutes at a smaller park where you can see everyone at all times. I prefer the ones where I can sit in the middle and see the whole park. When my kids were 3 and 1 I preferred the smaller neighborhood parks. Now that they are both able to run and climb, we hit the bigger parks and amusement parks.
Another thing we do every so often, especially with my son, is to let him get "lost". We did this a couple of times at the Wild Animal Park. He strayed a little too far ahead of us and a big crowd walked by us. We could see him, but he couldn't see us. We kept calling his name as if we couldn't see him. He got very scared and started crying. A VERY good learning experience for him. He remembers both those situations to this day, ESPECIALLY when we go to the Wild Animal Park. Now when we go some where and he stays a little too far away we remind him of what happened at the Wild Animal Park.