I am declaring foreign earned income, which I declare when I fill in 1040 through turbotax and I also fill it in line 1a when I fill form 1116. Is this correct?

I can't see your return to be sure, but this sounds correct.  Once TurboTax reconciles income to apply your tax credits, you will show as having earned income with the credit to offset some of your tax. 

 

With earned income, even foreign earned income, using this method you are still entitled to the refundable portion of the child tax credit.

 

The credit works on a bit of a bell curve - it is lower for less income and rises as income does until it begins to phase out at significantly higher income levels.