new to this era. Questions about phaetons or sedan convertibles?

[cobra5laddict]

l'm new to this era so i'm here to learn. I had a 28 roadster with a flathead and sold it. I have 2 kids and really missed having them with me to cruise around. im toying with the idea of a 4 seater convertible 32-40.
Ideally i'd prefer a 2 door car convertible that seats 4. Would that be a phaeton? or sedan convertible? Did such a car exist in 2 door configuration?

I'm hoping that the 32-40 era car will be a bit more suited for todays roads. the Roadster "A" was fun but took its toll on me after about 20 miles.