No, you will not have to pay the healthcare penalty for your mother in 2017.
Anyone on your taxes who is not a legal U.S. resident may qualify to have the penalty for going without health insurance in 2017 waived. This includes anyone who does not have lawful permanent resident status, known as a "Green Card".
In the Health Care tab of the TurboTax interview, you will choose the radio button for "I'll pick who had it and which months" on the page "Did you all have health insurance coverage in 2017?"
On the next page, leave the boxes for your mother blank and Continue.
The next page should be "Did anyone have a situation that waives the tax penalty for being uninsured?" On this page, you will choose the option, "Not a legal U.S. resident." This will waive the penalty for your mom.
