I am in Virginia and do not know if this would carry to your state, but.....based on what I know here in Virginia.....I would send in some small amount to child support enforcement to be counted toward the arrearage. Here in VA, you have to be 30 days behind before they will raise your garnished wage to make up for it....so, if you pay some amount you will not be 30 days overdue...and then she would only have one choice to collect that money..and that is take you to court....and then you could prove your case to the judge.
CSE is messed up!! DH got custody of ss last year. He was paying CS...well, CSE dropped their claim on CS for him, but his employer had already deducted a couple of payments and mailed them in after CSE had dropped it. CSE sent dh the money back...
But, when CS was ordered for BM to pay to dh....CSE put the amount sent back to DH on HER account. As if she had paid that amount when it was dh's own money. They will not correct this either, say they cannot adjust it....