Elderly person would like to go up to Mt. Hua.

I went there last Oct. and experienced the cable car. Personally, as long as she has no acrophobia or other aged diseases, it is ok for her to take the cable car to the mountain. There is enough space to have a rest on the mountain. Don't worry!
In spite of that, as there is a long journey to walk and many steps there, it is not suggested for your mum to walk too long.