Hello Marona
I'm sorry to hear of your Mother's suffering for all those years

My Grandmother was involved in a serious accident in early 1930s when there were so few vehicles on the road compared to today.
It would be very time consuming to look through the Barry newspaper archive without a better idea of the date of the accident. I think you asked whether you could borrow a library ticket on the other thread, and someone said they had looked at newspapers online. The Barry newspapers are probably on fiche and there is likely no index (online or otherwise) so it is a matter of someone looking for the specific article on fiche at the library. The library would be able to provide this service if the date can be more precise.
It is unlikely that anyone can find hospital records either as it's pre-NHS; I know Glamorgan Archives have Barry hospital records from 1950-on. With such a serious accident your Mother would have had months / years of hospital stays and out-patient visits. Perhaps she would have been transferred to a larger hospital to treat her, perhaps Cardiff.
Can you think of any other information that would help track down the date? For example were any of her siblings there too (or perhaps too young to go to the pictures)? Do you remember the film they had seen? That may help date the accident too....
I hope that you get more information about this sad accident.
Kindest Regards
Morgan