Your TAG might enjoy having her cage in an active area, as long as it's not TOO active, like thrown toys hitting the cage or something. Some greys can be bothered by the noise and fast movements of small children. You'll just have to monitor your new baby's reactions.
Wherever you put the cage, be sure at least one side is against a wall or some other solid barrier. This gives a bird a sense of security. Our CAG has his cage in the dining room in a corner, so it is nice and cozy. He can't see people approaching from one side of the open-ended dining room, but he doesn't seem to mind, as long as they don't startle him by rushing right up to his cage or something.
You will have to teach your smaller children that Rita's cage is her "safe place" and that she is to be left alone when she is in her cage. No poking things into the cage, etc. I'm sure I don't need to say that, really, since you have had a parrot before.
Can't wait to hear about Rita's happy homecoming!