They will take care of the transfer--we do split stays every summer. You can call bell services to come to the room to get it or bring it to them. Just be sure to keep anything out that you might want to use in the afternoon of the switch.
Since you could be without a room between check out and check in, you may want to use the pool, etc. Luggage doesn't usually arrive at the new resort until the afternoon. We made that mistake once--didn't think about it and our room was actually ready early but didn't have our swimsuits as they were in the luggage!
Once you get to the new resort and your room is ready, give bell services a call and they will bring it right up.