I've been using Yahoo mail for years, and it used to work fine before they "fixed" it.

They keep making "improvements" that foobar things.
I got very tired of the redirection to the home page, although never got your symptoms, because I marked *specifically*
as Untrusted, while allowing specifically mail.yahoo.com. Obviously, you can't do that if you use some of the features at the home page, but I don't.
I was still getting the annoying redirection, though somewhat less annoying than before. I wanted to get rid of it completely. Drastic solution,
use at your own risk (but it works): Navigate to your Hosts file (doesn't matter if you use a Hosts service or not): Windows > system32 > drivers > "etc". Make a backup copy of the HOSTS file, say, by copying it to the Desktop, in case anything goes wrong. Open the Hosts file, either by double-clicking or by right-clicking and open with Notepad or Wordpad.
Note the entry at the top,
which *must* always be the first entry. Anywhere below that, add
Save and close everything.
Now the computer *cannot* connect directly to yahoo.com. When you exit mail, you'll get the attempted redirection, then a "Can't connect" error message. Click "OK" and go about your browsing business. Annoyance eliminated.
You can still use subdomains of Yahoo: finance.yahoo.com, news.yahoo.com, etc. This is why it's critical to use the full domain (http isn't necessary),
http://www.yahoo.com. so that all other domains inside Yahoo are still allowed to connect, and you can allow their scripting if you choose to do so. You lose only that specific page, the home page/portal.
Strong measure, but it works.
Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.1.20) Gecko/20081217 Firefox/2.0.0.20