Private Road In HOA

We have a small undated community on a private road cul-d-sac that is maintained by our association.
We have children from the outlying neighborhood who don’t live in the complex, riding their bikes and scooters while their parents are taking a walk. There are other times the older children come without their parents.
Can we legally tell them they are not allowed to bring their children into the complex as it poses a hazard when people are pulling out of their garage?
We don’t want to make enemies, but there is a family with several children that the parents don’t supervise while walking with them and allow the children to run around ahead of them because we are not a through street.
We do have liability insurance for visitors but if a homeowner hits a child with their vehicle, they would be liable.

Sounds like your private road could be said to be an attractive nuisance for kids. Meaning that if some kiddo gets hit by a car, the victim's attorney will sniff around for the deep pockets, which means said attorney will at some point look to your HOA's insurance.

I would consult the HOA attorney about whether the road should be marked "no trespassing" yada and what you all can do to reduce liability.

We have signage at the entrance to my community saying essentially, "private street, residents only, no trespassing".

It won't completely keep trespassers out, but it can provide additional protection for the HOA when one of them gets injured.

Also: talk to your insurance agent to make sure you're adequately covered. Something apparently happened in my area and/or the law changed, because a year ago numerous communities sprouted "private street, residents only, no trespassing" signs.

I expect from your posting that the street is private (in that the Association owns/maintains the road) but with public access (not gated).

This certainly can become problematic.

However, it sounds like the issue is with children not paying attention (as they often do) while playing in the area and you are concerned of a potential accident if the driver of a vehicle doesn't see them.

In reality, there is likely little that can be done without fencing and gating the area (something I suspect you are not advocating). Therefore, the next best thing would be to minimize liability. This is why it has been suggested signage be placed in the area.

You can always address your concerns with the parents of those children, but, in my experience, that doesn't always go well.
No parent wants to be told how to parent, even if they are doing it badly in the eyes of many.

My understanding of trespassing issues will require everyone on the street to agree.
Our police department has told us:

1) if someone trespasses (salesman for example) - they have to be told about the no trespassing and asked to leave.

2) If they continue to trespass (go to the next home for example) - that individual has to tell them and call the police, informing the police that the individual has been informed once already and continues to trespass.

3) If the police can respond in time for the individual to still be around, they will do their thing.
If the police can not respond in time - they will need proof of the trespassing (video for example) and identifying information (business card as an example) to follow up.

Note - if the first owner doesn't inform the other owners and the next owner (who has to know the individual has been told) doesn't contact the police nothing happens.

So, in reality, the no trespassing doesn't work well for our area. However, signage does help minimize liability.