According to the IRS, parents who are not married and alternate claiming of a child dependent, "The parent who claimed their child on their 2019 return may have received an additional Economic Impact Payment for their qualifying child. When the parent who did not receive an additional payment files their 2020 tax return next year, they may be able to claim up to an additional $500 per-child amount on that return if they qualify to claim the child as their qualifying child for 2020."
This only references the one stimulus payment but would apply to both.
This is referenced in the last paragraph under Claimed dependents are not eligible for an additional $500 payment in this article: Why the economic impact payment amount could be different than anticipated
This will all be done by claiming the Rebate Recovery Credit on your 2020 return.
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