Firstly, you need to give your client a form W-10 giving them your name and social security number so they can claim the credit. This will trigger the IRS to look for matching income on your tax return.
Self-employment tax is 15% of your net profit (income minus expenses). Since you are married filing jointly, you need to look at your overall family income, and your federal income tax rate will probably be 12% or 22%.
https://www.cnbc.com/2021/11/10/2022-income-tax-brackets-and-standard-deduction.html
You don't need to think about your family deductions or credits because you will claim them anyway on your spouse's income. Self-employment isn't changing those, it's only adding income. So your estimates probably should be 27% or 37% of your net profit. Don't forget you may need to make estimated state tax payments too, I've seen state tax rates between 3% and 13% depending on the state and income level, you would need to look that up.
Now it's important to define net profit, or income from your business, because you pay tax on the profit, not the gross income. You will report your income on schedule C, and you can deduct business expenses. For home daycare, those expenses can include a portion of your rent or mortgage, a portion of your utilities, an allowance for meals and snacks, and other things. See this for full information.
https://www.irs.gov/pub/irs-pdf/p587.pdf
So if you track and document your expenses, you can reduce your gross income by subtracting those expenses, and pay less tax overall.
