Taxes are complicated. There isn't a simple formula for calculating that amount.
You both have to prepare your returns both ways and compare the results. That's hard to do with the online software.
The two main elements of the child benefits are the child tax credit (Up to $2000) and the Earned Income Credit (looked up in a table)
https://apps.irs.gov/app/vita/content/globalmedia/earned_income_credit_table_1040i.pdf
You could try this tool, for comparisons: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1
This year there's the additional complication of the stimulus payment. Alternating year parents both get it, but if one of you claims the child both 2019 and 2020, only she gets it. That's $1100. Amending may be best.
