Then log out of the sit and stay on the forum one until you must access the chat, since that's the one and only function that the forum doesn't have at this moment. I myself just use the forum login unless the site chat calls.
The other login next to the banner doesn't work quite the same as a regular forum login, probably why you need to reload the page a few times and login again.
You don't really login twice, I'd say, just the forum being able to catch that you actually get signed in to it. Also should try to make more suiting text in your post and titles.