It seems to me from the description of the steering swinging out with the front opening door, that you are in fact describing not a FIAT but a BMW ISETTA.
This was an Italian design but German built car with a 300 cc air cooled single cylinder. I owned 2 years ago in the UK. As it had 3 wheels you had to pay only motorcycle road tax. It was practical transportation but I nearly rolled it several times.
I have also owned FIATs and have enjoyed them . The car that I have owned that was the most fun to drive was in fact a FIAT 128 coupe. Drove just like a go kart!
Memories from the past!
Steve Cotsford