I’m so sorry for you both, it can be so hard helping children through these things. I suspect that this has very little to do with you using a walking stick and is just about her fear of “losing” her mum! In which case what ever we suggest about the stick will make no difference.
When I was confined to my bed for month, after a bad fall, my five year old granddaughter (to whom I’m very close) wouldn’t come near me for two weeks. She would peep round my door but wouldn’t come in or talk to me. I realised that she thought I had taken to my bed and was going to die, as my mother had done a year before. We had a long chat and she then got back to normal but she still needs regular reassurance.
I’m sure that you’ve had all the necessary conversations with her about MS but may be she’s worrying about something that she thinks you might think is silly or that she doesn’t want to up set you.
If it really is just the stick that is upsetting her perhaps an elbow crutch would bother her less. Lots of people, including users, feel that a crutch says injury or illness rather then old age. I find a crutch/es much more stable and convenient than a stick/s but it’s taken me 20yrs to realise the advantages!
Sending you both huggs xx