Whoever claimed the dependent on their 2019 taxes should have received the stimulus checks, also known as economic impact payments (EIP). However, the spouse who claims the child on a 2020 tax return may also be able to claim both of the additional stimulus payments ($500 for EIP1 and $600 for EIP2) via the Recovery Rebate Credit (RRC).
Only the parent who claims the child on their 2020 tax return can claim the child-qualifying portion of the RRC. The dependent must also be age 16 or younger for the entirety of 2020 for you to claim the credit.
Similarly, the parent who most recently claimed the dependent gets EIP3. Only the parent who claims the dependent on their 2021 tax return can claim the RRC for any missing EIP3 funds.