Heres my setup to prevent sent msgs in gmail from appearing in the iphone's inbox.
Setup a filter in gmail to forward all msgs from yourself to another email and also select delete emails from yourself. Now at the other email you are forwarding gmail sent messages to, create another filter to sort all messages from your gmail address into a custom folder.
This way you can freely send messages from your iPhone or gmail web client and have those messages be sorted and saved at another email. Not perfect, but gets the job done for the time being
Setup a filter in gmail to forward all msgs from yourself to another email and also select delete emails from yourself. Now at the other email you are forwarding gmail sent messages to, create another filter to sort all messages from your gmail address into a custom folder.
This way you can freely send messages from your iPhone or gmail web client and have those messages be sorted and saved at another email. Not perfect, but gets the job done for the time being