First of all, she is almost 18, so no one needs to tell her anything when it comes to making conclusions
As another post mentioned, SHE cannot legally pursue this. YOU can period. Being mad etc., was a stupid move by your ex-husband. YOU can/should contact your local Child Support Enforcement Agency.
After you fill out the required documents, they will open a case agianst your ex-husband, and work their "magic" to recover the court ordered child support arrears payments to you.
The bottom line: Only YOU can start the process, as the money is owed to you (for her expenses), not her.
I'm not a lawyer. This is only my opinion /suggestion. Most Replys' are based on information provided by the "original post" (OP).