Upvote:4
It is impossible for anyone to accurately answer the question without seeing your mother. The rules are based on how well she fits in the seat in question and whether the seat belt fits her.
United rules are spelled out on: http://www.united.com/web/en-US/content/travel/specialneeds/customersize/default.aspx
But the two biggest factors, can she fit into the seat with both armrest's down and can she buckle the seat belt around her with a maximum of one extender.
Compounding the issue is that different aircraft have different width seats and likewise there are different length extenders. So a lot of the judgement calls will be made planeside and there is no real appeal process.
If she is very broad in the hips and abdominal areas and the airfare is not out of control, why not buy her the extra seat, making her flight (and her row mate's flight) more comfortable.