Why hasn't she applied for Attendance Allowance (AA), from the little said in the OP I would expect her to qualify. Make sure you contact Age UK or other charity for the elderly for help and advice on how to complete the form. The questions are deceptively simple and catch people out.
The hints I would give are 1) If the applicants verbal response to a family member or similar about anything they do is 'I manage' or 'I cope' or similar, then they have a problem, they then need to describe how they cope - 'I hold onto the bedside table as I get out of bed to stop me falling', for example.
2) repeat yourself again and , again in every question 'I cannot get in and out of ber, climb stairs etc tc because of my arthritis.
3) Always describe how you are on your worst day.