My ex-wife received the advanced child tax credit. I will file my child for 2021 taxes. Do I have to take the hit for the advanced money my ex-wife received?

You will be able to claim the full amount of the Child Tax Credit for your child on your 2021 tax return even if the other parent is receiving advance Child Tax Credit payments. The other parent should have unenrolled  from receiving advance payments, but their decision will not affect your ability to claim the Child Tax Credit.

The other parent that is receiving the advance child tax credit payments will need to pay it back to the IRS if they do not qualify for repayment protection.

https://www.irs.gov/credits-deductions/2021-child-tax-credit-and-advance-child-tax-credit-payments-t... 

https://www.irs.gov/credits-deductions/2021-child-tax-credit-and-advance-child-tax-credit-payments-t... 

No. You will get the full amount when you file your 2021 return if you claim the child. Depending on her income she might have to return some of the payments that she received. 

If you are not the parent who had custody more than half the nights of the year, make sure you get a signed form 8332 from the other parent.  You must mail the signed original to the IRS after e- filing.  

You will also likely qualify for a $1400 round 3 stimulus payment, assuming the round 3 payment for your child was also paid to the other parent earlier in the spring.  Unlike the child tax credit, she will not have to repay the stimulus even if you also qualify when you file.