Your spouse has self-employment income. The child's parents do not have to issue a W-2 or a 1099. But they will need your spouse's Social Security number or her Tax ID in order to get the childcare credit. They can take that credit if they paid her to care for their child so they could work. If she does not want to give out her SS number she can get a Tax ID from the IRS and give them that number to use on their tax return when they claim the credit.
https://www.irs.gov/individuals/individual-taxpayer-identification-number
Your spouse will need to pay self-employment tax for Social Security and Medicare. If she has any expenses she can prepare a Schedule C. There are often expenses incurred by nannies and babysitters that can be claimed on the Schedule C.
https://ttlc.intuit.com/questions/2926899-how-does-my-side-job-affect-my-taxes
https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/...
https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922
https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax
https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c
https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct
https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
