Dude. Just load both SIGNED applets with the same world. Enter your name/pass on one applet, and your other name/pass on the other. If you click 'login' on one, then click 'login' on the other it will still work IF you do it quick enough. You have to do it in about a half-second (Which isn't too hard). I suggest you adjust the size of each window so that the 'login' on one is literally a few pixel's from the 'login' on the other. Then, click one, click two, and your in. It sounds confusing but it's not.
I don't suggest you use tabs because it's takes too long to switch to the other. Use two seperate windows. When your logged-in, go ahead and restore the windows to their normal size.