You could check with the court if they would allow this relative to come down and accept responsibility for the tickets.
This is not legal advice. If order to give you legal advice i would need to see the Tickets and talk to the court first. Good luck:)
Have you considered other options to the 50% down payment, such as bankruptcy relief? Presumably the relative who caused the problem can't help you with the 50% payment.
For income eligible persons there are legal aid organizations that might help with a bankruptcy filing.
The information provided here should not be construed to be formal legal advice. The provision of this general advice does not create a lawyer-client relationship. Persons with legal questions are encouraged to seek independent counsel for advice regarding their individual legal issues.