Mom is depressed and agitated every time she is left alone. Any advice?

Mom is 90. She lives alone. My sister is only 4 miles from her house and I am 15 miles away. My sister sees mom up to 20 hours a week and I am there on average about 8 hours a week. We also hire a person to take mom out twice a week for an average of 8 hours per week. With all this help, mom still calls me crying that she doesn't know what to do with her life. She is distraught about having to sit alone on her couch for the hours that remain between care giving and the rest of the time. No matter what we do, it never seems to be enough. Mom wants to spend the rest of her days in her own home, but really only wants family around her and resists outside help. Sister and I are not in a position to take mom into our homes. Neither sister nor I want to make mom feel abandoned but we can't give up our lives to satisfy mom's wish to have her family around her 100% of the time.