As you amend the return you just need to add the child as a dependent to get the other dependent credit.
Look at the form 1040X …
Column A should have the figures from the original return, Column C the corrected figures and Column B the differences between the other 2 which needs an explanation on page 2 of the form 1040X.
If you completed it correctly you will see an entry on either line 16 OR 18:
On line 16 should be the amount you paid with your original return. If you paid nothing already then this line should be zero.
On line 18 should be the amount of your original refund you received. If you have not received your refund yet then you need to wait for it. If the refund changes from what you expected then this line must reflect that change.
Then you will see your extra refund on line 22 OR the new balance due you need to pay on line 20.
Here's another way
You must have a copy of the original tax return you want to update (or a transcript).
The simplest way is to prepare your correct tax return (using TurboTax for example, or other means) and print it.
Then lay the paper printouts of both returns (correct and original) side-by-side.
You now have all the information needed to prepare Form 1040-X by hand.
It's pretty straight-forward (if you are not form-challenged).
The blank form in fillable PDF format and its instructions are available at www.irs.gov.
Refer to the Instructions for what is to be attached to Form 1040-X.
Do not include your old 1040 nor your revised 1040 because the Form 1040-X reflects any changes there and becomes your new tax return.
Mail to the address shown in the Instructions.
If your Earned Income Credit changes, that goes on 1040-X line 14.
If your EIP Rebate Credit changes, that goes on 1040-X line 15.
Select Other (Rebate Credit).
Otherwise, for no change, Column B should be zero.