If you want to sue your neighbor to force him to repair the fence or help you pay the cost of repairing the fence, then you will have to show that he has a shared duty to do so.  Even though the HOA says it's your problem, you can use HOA restrictive covenants to prove that they have a duty.  If there is a rule that all homeowners are required to keep their fences in good repair-- then you could sue to enforce that duty to repair.  If there is nothing in the HOA rules and no restrictive covenants on his deed that went with the HOA, then you're going to have a hard time doing anything to the homeowner.... especially since it would be a joint obligation and you have the same duty.  If you don't want your children at risk then you will have to repair the fence yourself.   If you do decide to file a suit, get a couple of quotes from property attorneys to help you-- to make sure that this is even a cost effective option for you.