When you file married filing separately you are not eligible to get EIC.
The tax laws for EIC changed for 2021 and will change again for 2022 returns, but if you are a married couple making over $100,000 between you, you are not going to qualify for earned income credit.
The "child tax credit" is a different credit--not to be confused with earned income credit.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/qualifications-ea...
This information is for tax year 2021---for tax year 2022 the child tax credit reverts to $2000 per child under the age of 17.
https://ttlc.intuit.com/questions/1900923-what-is-the-child-tax-credit
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