Unfortunately, while you are in arrears your refund can be taken for the child support. The components of the refund are not separated. If you have a refund it can be taken until this matter is cleared up.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
If there's an arrears, and it's through the IV-D system; then depending on how much you owe, they can (and do) intercept it. If you take steps to address your arrears, you can avoid this nasty annual surprise. Contact a family law attorney in your area for specific guidance.
If you owe more than the refund is worth, they can take it. You can file for Injured Spouse Relief for your wife, and then she will receive her portion of the joint refund every year. Technically, none of your income, credits, and deductions are related to the other children. That is not what determines whether it is subject to tax. There is no "deductions and credits related to new children" exception.
If you file Married Filing Seperately, you will lose out on many of those credits anyway. They simply will not let you shift deductions and credits to the lower earning spouse. So if you file Married Filing Seperately, you both must take the standard deduction, and most credits will be disallowed.