My mom passed away Sunday December 18th 2016. She lived with my sister but I took her to all her chemo appointments. Her blood transfusion appointments and even spent countless hours sleeping at the hospital with her.
Unless your Mom was your dependent or you were a paid caregiver, the gas or mileage expenses are not deductible for most cases. As suggested above, check with tax preparer familiar with you, your mother and your sister's situation.
Your question is one that I would present to a CPA or a tax person.