I note from your profile that your mother had ataxia, but before that, she had a cough.....
There is a type of ataxia, so far discovered in Anglo-Celtic and Portuguese families, which has a cough long before the ataxia starts. The cough tends to fade after the ataxia sets in. There's no specific gene test yet, but the theory is it's related to SCA20, as there's a link to genes on Chromosome 11 (where SCA5 and 20 are found), and on MRI they can also show certain changes in the core of the cerebellum (calcification in dentate nucleus). Scroll down to see the description of the cough:
It seems fairly mild, as in one family, only one family member ended up in a wheelchair after 40 years of ataxia, the other were still fairly mobile:
Of course, she might just have had swallowing and coughing problems as an early symptom of ataxia, and it just wasn't picked up as being that, but misdiagnosed as something else.
To compare other conditions, they seem unlikely. Other links between coughs and ataxia would include the lung disease which can occur in Ataxia Telangiectasia. However, it's recessively passed on, so unlikely you and your mother would both have symptoms - your mother would usually have been an unaffected carrier:
A-T above overlaps with Cystic Fibrosis, which can affects the lungs, liver and gut. But it's also recessive, so unlikely both you and your mother would have had symptoms. CF can stop absorption of Vitamin E in the gut, and the Vitamin E deficiency can cause ataxia. Treatment is by providing supplements of Vitamin E:
Various other lung diseases might be coincidental. But Lung cancer can obviously cause coughing, and in some cases can lead to PCD (Paraneoplastic Cerebellar Degeneration), where anti-cancer antibodies cross-react with the cerebellum. If so, this might possibly mean you and your mother's ataxia were unconnected (red herring?).
So, of these, if none of the others seem to apply, that SCA20 link sounds the most interesting one, in which case, maybe you could make a copy the article and ask your Neurologist about it. :-)