I've been using Gmail for many years now and almost exclusively through the native Macintosh and iOS client software, Mail....always configured for IMAP....rarely accessed by web interface using a browser....never with the duplicate inbox issue for sent mail that you are experiencing.
(Your duplicate issue may be a miscue in the default preference settings....)
In the rare times that I've been forced to use the web interface for access to read or send an email, I have seen VERY different results between differing browsers (mostly on Windows public shared use computers because I had no available internet access using my own computer).
When accessing Gmail from my own computer (and iPhone) using the native client I have seen very little interference or issue.....in other words, "it just works" seems to be applicable in my experience.
All in all, a brief search of the App Store yielded no real solid third party candidates to replace Mail as the native mail client on my machine....all reviews that I saw included that level of instability you expressed concern with earlier.
