I would say that if you wrote to them and confessed to them that the letter you wrote to them was a lie, then they will come after you for the entire sum.
You see if you contact them admitting to one lie, and if your ex is contacted about the matter, then it will be your word against hers and you will be the proven liar.
All she has to say is that you are jealous and this is revenge.
Given that she has a child to look after and that they will of course take into account the ramifications of the allegations you are making against the child's Mum, on that child, I would say that you would be the best target.