You should contact your Probation Division Case Manager. The expenses that you pay for your child when she is with you may be deemed voluntary contributions by a judge and you will still owe how ever much child support is currently due. You can request that Probation contact the Judge and suspend and/or vacate the warrant pending the application to modify support that you NEED TO FILE immediately. This way if you get picked up and brought before a judge, you can tell the enforcement judge that you filed an application to modify support and they most likely will not put you in jail and await the outcome of your motion.
Should you need help filing the motion, please contact me. My contact information is on my profile.
Lastly, the 4 to 15 days a month that your child is with you, are they overnight visits or just daytime visits because that is a big factor in the child support calculations.
Your should take affirmative action, as opposed to sitting back. You can start by contacting the Probation Department to see if it will consider modifying the action it has previously taken. Alternatively, you must file a Motion with the court. Within the Motion you will request that the Warrant be Vacated; you can seek a modification of the support obligation. Lastly, you should be prepared to make a payment toward the arrears that have been deemed due and owing. It would be in your best interest to be prepared to satisfy the total arrears due.
In the event you recognize that the arrears are due and have the ability to satisfy the same in full you can simply go to the Probation Department, make the payment in full and the Department will take action to vacate the Warrant.
The Answer provided was based on the limited information provided, and represents information based on the law in general, not a legal opinion that can be relied upon. Before a formal legal opinion can be offered I would need an opportunity to review all possible relevant facts and circumstances. You cannot rely on the advice of an attorney given over the internet. The exact facts of your sitaution, including facts which you have not mentioned in your question, may completely change the opinion that is being offered. Please be aware that the above comments are neither protected by attorney-client privilege, nor may the same be the basis for a malpractice lawsuit.