Virgie Arthur, the mother of the late Anna Nicole Smith, wanted to prevent Birkhead from taking his child outside the country before the next custody hearing in June, but her request was denied.
The judge reportedly said he was "a little perplexed" as to "why this order is in front of us," adding he felt it was "weak" before denying the appeal.
Arthur also also ordered to pay court costs of $3,000, including Birkhead's fees.
This was an "expensive day for her," said Birkhead afterward. "I feel like I just got a divorce from her, and I didn't even know we had a baby together."
He planned to take Dannielynn back to his home in Louisville.
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