It depends. Back Child Support is one reason the IRS may offset, or take and apply your refund to satisfy an outstanding debt. If the back child support you owe is greater than your refund, you won't get back any of the refund. Your wife may get back a portion of the refund if you file an Injured Spouse return by submitting Form 8379. Otherwise, the only way any refund is issued is if the debt is satisfied by the refund and there is still refund left over.
In that case, the remaining refund is split the way you have defined. If you are splitting 50/50, she should get half of what is left over and you the other half.
If filing an Injured Spouse Form is in your best interests, please see this FAQ: https://ttlc.intuit.com/replies/3326788
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