They do not need to give you a W-2, even for them to claim the dependent care credit (DCC). Since you sat the kids in their home that makes you a household employee and not a self employed person. But because you are the parent, of the taxpayer, you are exempt from the "nanny tax". That is they don't have to pay social security and medicare (FICA) tax and neither do you.
You will file the income as a Household employee. The money goes on line 7 of form 1040 (or 1040-A) with the notation "HSH". It's a little tricky entering in TurboTax. In TurboTax, enter at:
Federal Taxes
Click on Wages and Income
Click on Explore on My Own
Scroll down to Less Common Income
On Miscellaneous Income, 1099-A, 1099-C click the start button
On the next screen click the start button on Other Income not already reported on Form W-2 or Form 1099
Answer Yes on the next screen and enter the amount under Household Employee Wages
Three side notes:
1. A parent (as a Household Employee) is exempt from Social Security and Medicare taxes UNLESS they are watching the child and the parent is divorced (and not remarried) or widowed.
https://www.irs.gov/publications/p926/ar02.html#en_US_2014_publink1000867402. You MIGHT not be required to report this as income at all, because it is only a transfer of money between family members, and could be considered a gift, under the right circumstances. But, in order for them to claim the day care credit, you must report it as income.
3. If the amount is less than $10,300 ($6200 if you are claimed as a dependent on someone else's return) and you are not filing a joint return with your spouse, you do not need to report the income at all, even if the parents are claiming the DCC. But because they are claiming the dependent care credit, they will have to provide your SS# to the IRS. There is a small chance that you will get a letter, from the IRS, that you will have to respond to. Hopefully, you can explain it away, with the facts.
