I use to be a moderater to a forum exactly like this one ( not parenting though)
We had it set up so when the person signed up not only did it record the IP address but put in a sort of cookie. the person could not sign up with another account until writing to the moderater ( the admin and me) the reason to other account. It recorded how many times they tried to make a new account and if it was alot and there excuse was lame we banned them.
I didnt do the download so unfortunately I do not know what it was. You could ask about it in the admin forum for this set-up.
Its one of the updates.
The other thing to do is make a trash place its easier to keep evidence for disputes and the moderaters just o move the post or threads to trash. They can be hidden to the public and visible to mods only ( if its not already that way