Under current guidelines you both would be able to get credit for the child stimulus payment as long as the child is age 16 or younger. Whoever claimed the child (age 16 or under) in 2019 would have received the child stimulus payments based on that tax year return. If parents are alternating years then the other parent would also be able to claim the child (age 16 or under) on the 2020 return and get the Recovery Rebate Credit.
However, if the child turned age 17 in 2020 and that is the age showing on the 2020 tax return, then the child will not be eligible for that Recovery Rebate Credit child payment.
Custodial and non-custodial issues are not addressed by the IRS in the Recovery Rebate process.
Here is a link with more information on the Recovery Rebate.
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