Form 8814 is not the problem. The reason TurboTax told you that the child's income does not have to be reported is that you did not enter the Alaska Permanent Fund Dividend correctly. On the screen where you enter the amount, note that the description for the box where you enter it says "Alaska Permanent Fund Dividends (included in "Ordinary Dividends" above)" [italics added]. You must enter the PFD amount, $1,600, in both the first box, "Ordinary Dividends," and in the box that says Alaska Permanent Fund Dividends. See the screen shot attached below. When you enter the amount in both boxes, TurboTax will handle it correctly. If you don't enter it in the Ordinary Dividends box, TurboTax thinks the child had no income, so it tells you the child does not have to file.
Form 8814 is not the problem. The reason TurboTax told you that the child's income does not have to be reported is that you did not enter the Alaska Permanent Fund Dividend correctly. On the screen where you enter the amount, note that the description for the box where you enter it says "Alaska Permanent Fund Dividends (included in "Ordinary Dividends" above)" [italics added]. You must enter the PFD amount, $1,600, in both the first box, "Ordinary Dividends," and in the box that says Alaska Permanent Fund Dividends. See the screen shot attached below. When you enter the amount in both boxes, TurboTax will handle it correctly. If you don't enter it in the Ordinary Dividends box, TurboTax thinks the child had no income, so it tells you the child does not have to file.
What is "it" that tells you the children do not need to file? That is not correct if your children are your dependents. For 2018, a dependent with unearned income over $1,050 is required to file a tax return. Since the 2018 Alaska PFD is $1,600, every dependent child who receives a 2018 PFD is required to file.
(You might have the option of reporting the children's PFDs on your own tax return. Doing so would satisfy their filing requirement.)
The desktop editions do not have the Form 8814 finalized. If the user goes through the Child's Income section under Less Common Income the program indicates the child does not need to report the income, which is incorrect.