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It sounds like your dependent child does not have to file the tax return or 2012. You are correct that the test is unearned income greater than $950. The K-1 showed less than that, so no tax return will be required as long as that is the only income item for 2012 for the dependent.
The rest of the distribution is tax free and will not impact the $950 income threshold. It happens often with complex trusts; that distributions can exceed the taxable portion. The excess does not trigger the filing requirement, nor is it taxable to the recipient (the K-1 says so).
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Great thank you. Confirmed what I thought.