My dependent Child received a 1099-DIV, but Turbotax does not let me assign a 1099-DIV to a dependent child, only myself or spouse. How do you assign to a dependent?

You need to look for Child Income.  I don't know where that is.

Report child investments income

https://ttlc.intuit.com/community/investments/help/how-do-i-report-my-child-s-investment-income/00/26623

If his only income is from interest and dividends, Alaska PFD or capital gains distributions shown on a 1099-DIV, there is a provision for entering it on your return, using form 8814. Enter at Less common income / Child's income.
But, it is usually best for him to file a separate return, as qualified dividends and capital gain distributions could be taxed at a higher rate on the parent's return.