The first and second stimulus payments are reconciled on the 2020 tax return. This means that you would be entitled to the stimulus for your child if you claim your child as a dependent on the 2020 tax return. It's up to you and your spouse to decide who will claim your child on the 2020 tax return.
It's not clear why your spouse did not receive a stimulus for your child based on the 2019 return, but there will be no recovery for anticipated stimulus because the 2020 return will be used by the IRS at this point.
You can choose to file jointly or separately and I would advise to check both ways and include the stimulus to see which comes out best. Likewise you can file separately claiming your child by testing each return to see which provides the best result.
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