I'm a retired police officer and I think that you are wise to not let your daughter go to the playground unsupervised by an adult especially if you don't live in the safest area and the adults who live across from the playground are not involved.
A couple of days ago I left my 8 yo granddaughter at the apartment playground playing with other kids who live in the apartment. The apartments are city or county affordable housing and I've seen that most of the children lack supervision. I was away from the playgound for about 10-15 minutes twice. When I returned the first time my granddaughter came running to me, crying. She said that she was playing ball with 3 of the boys and that they were throwing the ball so that she had to run for it and then laughing at her. The boys are close to her in age.
When I returned the second time she was running away from the playground, again crying. She was covered with chocolate drink that she had shared with the boys. Each had their own can. I'd seen them sitting together talking and drinking the drink peacefully. The boys had no chocolate on them but they said that she started it. They were in the process of pouring the drink on the sidewalk and on the playground equipment.
Neither of these experiences were life threatening but I will stay with her the next time she's on the playground. Last summer her mother befriended an older boy, 10, and asked him to keep an eye out for her. That seemed to work.
I have always been concerned about kidnapping even tho the playground is in the middle of the buildings. Strange cars use the driveway as a turn around. I just don't think that kids are as safe as they were when my daughter was growing up 20 years ago. Even then she could only play with friends in our yard or their yard. I called the parent and told them that she was coming over and she called me when she got there. She and none of her friends were allowed to play anywhere that there was not responsible adult supervision. This meant that we parents all knew each other.
As a teen she could walk to the local park about 6-10 blocks away with a group of friends but we parents stuck with the no playing at someone's house without responsible adult supervision.
When she was around 12 I dropped her off at her friend's house and talked with the father and older sibs. Everything seemed alright but my daughter ended up hurt badly enough that we filed a police report. I was a little uncomfortable leaving her there because I didn't actually know anyone in that neighborhood but I thought that she was mature enough to call me if there was a problem. She didn't call. She didn't want to be called a sissy. This was 20 years ago.
I think that you should follow your instinct and not let her go to the park unless you're able to arrange good safeguards. At the same time I also know that she needs to be able to play outside. It is not good for her to be in the house all of the time.
I'm wondering about your 17 and 15 yo kids. Are they not responsible enough to be on the playground with their friends at the same time as your daughter?
My daughter is a full time working, single parent and during the good weather she spends a couple of evenings a week, an hour or two, with her children, 8 and 5, at the neighborhood playground. They walk there which gives them more exercise which is good for my daughter as well as her kids. They also live about 6-10 blocks from their neighborhood park.
I think it's important for all of you to develop you get exercise. Perhaps you could start out going as a family and then take turns going with your daughter. If your older kids are "typical" teens and don't want to do this and/or you don't think that they would be responsible for their little sister perhaps you could have them do chores at home while you went with your daughter. They could fix dinner, wash up after, or any of the assorted chores you're doing in the evening. You could take a book or other hobbie activity with you along with your daughter's friends to keep her busy.
I know it's difficult ensuring our children's safety in today's crazy world and to also provide plenty of outdoor activity but finding a way to do so is as important as providing nutritious meals. I hope that you find a way that feels acceptable to you.
An added thought. Could you arrange a block party involving the parents of your daughter's friends as well as those people living across from the park? Talk with everyone about making the neighborhood safe for everyone; especially the children.