Not that the Dark Horse comic DOTS is on my favs list, actually it is one of my most disliked of all time, but it had one redeeming panel, showing a Queen Alien running holding an egg with its secondary arms. Not canon, obviously, but it is a good idea.
The second set of arms could be used to take an extra egg with her, if there is a viable on near by, if she has to leave the hive in an emergency and there are no regular Adults near by any more.
This way her larger more proportionate primary arms set are freed up so she can function more or less like a giant sized regular adult without having her hands full.
This does not discount the possibility of the ability to lay an emergency egg, but is just another survival characteristic of the Queen, and a good use for the secondary arms.