In Chrome, I signed out of DU and then opened DU in two tabs, both signed out. I went to a thread in the first tab, then signed into DU in the second tab, then went back to the first tab and clicked reply (without refreshing the page) and it proceeded as if I was signed in, correctly sending me to the reply page.
I then repeated the process in Firefox and got the same result -- after signing into DU in the second tab, the browser recognized that I was signed in on the first tab when I clicked the Reply button, without a page refresh.
That's the way I assumed it would work, so unfortunately I'm not sure why it's not exhibiting the same behavior in your browser. Clearing your DU cookies may help, but beyond that, I'm not sure what the issue could be.
The second problem you describe -- you sign in and then use the Back button to go back to a previous page, then perform an action that requires you to be signed in, and are sent to the sign in page again -- actually sounds like it makes sense, given the first problem. If you are signed out and click the Rec button you will be sent to the sign in page. After you sign in, and then use the Back button to go to back to the thread and click the Rec button again -- without a refresh -- the page is essentially in the same state as it was before you signed in. So you get sent to the sign in page again -- however, once the browser reaches the sign in page, the server recognizes that you are already signed in (because you are already signed in) and so you get the "already signed in" message.
The bottom line is that any time you are signing into DU in one tab and then continuing browsing in another, or any time you sign in and then use the Back button, it could create a problem where the browser doesn't correctly recognize that you're signed in. The simplest solution is to just hit Refresh after you switch to a new tab or use the Back button after signing in, to make sure your browser recognizes that you are already signed in.
= new reply since forum marked as read