World 2 is currently full, so I don't think your daughter can join you there. Maybe you can both make new accounts in World 3, or wait until World 4 ?
Yes, I just checked for you - registration is not currently possible on world 2 as it is full.
As for the problem with world 3 - you say she logged in as your character ? Check again. Try making a new account with her email in world 3 and selecting another name, I think the default if you already have a character is the name employed in the previous world.
I actually choose to play as Rose of Alabama in both world 1 and world 3.