Will my ex not get her refund if I owe the IRS on my amended filing?

I accidentally claimed our son this year. Her return was rejected because of this. I've already filed my amended (1040X) to fix the mistake.Now that I don't get the deduction, I owe the IRS money. The question is; will my ex not get her refund until I've paid the full balance of what I owe to the IRS on this amended return?

I don't think this is the case, but I don't know. Thanks for any help you can give me.