I just switched my opening folder from inbox to sent mail.
Turned my phone off, restarted went to Yahoo mail and it opened with sent mail still.
Just switched back to inbox.
Yours should be working this way also.
Can you switch it on other mail accounts.
I can switch opening folders on my gmail, cox and exchange mail accounts also.
I set up my Yahoo account up by clicking add account and then chose yahoo mail from the list.
Don't think it would make a difference but I am on tmobile network.
The question is, does the OP have a standard app icon on his home page, or a widget?
I haven't used Yahoo mail for years (frankly, I think it sucks, but that's another story for another day), but using GMail as an example, a standard icon will take you to your default folder whereas a widget can be set to open to any specific folder.