Here's why I suggested that trike kit over a cheaper geared motor.
You pointed out that this woman is elderly. So her being elderly is apparently a factor in your design consideratyions. Since I'm taking care of an elderly person and aware of some of their needs, I put one factor above the others. Reliability. it needs to work every time, from the time they leave, until the time they arrive home. No issues, no hiccups, and certyianly no breakdowns that would leave them in a bad situation. If the elderly person I know was stuck on the side of the road on a 100 degree day, it would be a life threatening situation.
10mph is slow. there are some slow geared kits, but they tend to be gutless. Assuming this person may need the full benefit of the motor sometimes, a motor designed for slow operation is a better idea, and there aren't many slow wound motors available anymore. The trike kit is about it. it has the added advantage of only 1 moving part.
Reverse. Because backing up and trying again solves many problems that a younger, more able bodied person would just get off the bike and push, pull, or life to solve.
And last I recommended the mobility scooter SLA for reliability. there are plenty of Ebike SLA out there, and they have the reliability of a paper boat in hurricane. Something designed to push an mobility scooter or electric wheelchair is going to be more reliable.