If care is provided in the provider‘s location, they are self-employed or an independent contractor and you are not responsible for their tax return in anyway. However, you must provide their Social Security number when you claim the credit. If the IRS does not see matching income from them on their tax return, the IRS make investigate them. But you would never owe their taxes.
If you don’t have their Social Security number and they refused to give it to you, the IRS may allow you the credit, but they judge this on a case by case basis. And they will use the information you provide to identify the provider and investigate them.
Whenever you engage a private daycare provider, you should always have a talk up front about taxes. If the person wants to be paid under the table, and you are not OK with that, you should not use them. They may be charging you a lower rate because they expect to not pay taxes. If you insist on claiming the credit, you need to agree up front and get their Social Security number up front, and if they know they are going to have to pay taxes on the income they may charge you more for daycare.
