@serhatyal
Regarding wages paid to your parent:
Your parent is still a household employee, not self-employed, if the care was provided in your home according to your directions. If you do not issue a W-2 (because you did not withhold tax and they are not subject to social security and medicare withholding) they are still required to file a tax return. When they file, they put their wages on line 1 of form 1040 with the notation "HHS" next to the amount. This is true whether they are residents or non-residents.
As a resident, they would be entitled to a standard deduction (in most cases) and if this was their only taxable income, they would not owe tax (in most cases). The rules for non-residents are different. If your mother reported household employee wages on a 1040-NR, she might or might not owe taxes. I don't know the rules for form 1040-NR. The filing threshold is not $400 (that is for self-employed) but I don't know what it is. Again, if she is thinking of immigrating instead of visiting, one of the questions is, did you pay taxes that you owed? While your grandmother might be able to get away with not filing a tax return for the household employee wages, the risk and consequences would be up to her to evaluate.
Regarding you claiming the credit:
Yes, a parent or grandparent is an eligible caregiver. However, you are required to obtain the caregiver's tax number. If you want to claim the credit without the caregiver's tax number, you can't e-file. You must file by mail and attach a written explanation. At that point, the IRS has the discretion whether or not to allow the credit. Remember that under the US tax law, all deductions and credits are "matters of legislative grace" and the IRS does not have to award any deduction or credit that you can't prove.
If you choose to treat the payment as wages, you will have to file by mail, attach a written explanation, and see if the IRS accepts it.
See these instructions for form 2441
Complete columns (a) through (e) for each person or organization that provided the care. You can use Form W-10, Dependent Care Provider's Identification and Certification, or any other source listed in its instructions to get the information from the care provider. If you don't give correct or complete information, your credit (and exclusion, if applicable) may be disallowed unless you can show you used due diligence in trying to get the required information.
Due Diligence
You can show a serious and earnest effort (due diligence) by getting and keeping the provider’s completed Form W-10 or one of the other sources of information listed in the instructions for Form W-10. If the provider doesn't give you the information, complete the entries you can on line 1. For example, enter the provider's name and address. Enter “See Attached Statement” in the columns for which you don't have the information. Then, attach a statement to your return explaining that the provider didn't give you the information you requested.
