We did this last year! We split our stay between Caribbean Beach and the Grand Floridian and had an AWESOME time!

I have pictures of our vacation last year on my "family vacations" web site, the link is below in my signature.
We stayed at CBR first then switched to GF. It was extremely easy and took only a few minutes to check out, then check in at GF. We LOVED CBR, in fact, at first my sons didn't want to leave to go to the Grand Floridian! But once we got to our room at the GF, they loved it, and it was so much fun to be on the monorail and have that view of the castle from our balcony
I have to say though, the bus service was MUCH better from CBR than from GF because GF shares bus service with the Polynesian and the Wilderness Lodge. This didn't bother us because we just relaxed and enjoyed the rides.... but some people really don't like long bus rides. So if you do split your stay, try and do MGM, AK, etc while you're at the moderate, then do MK and Epcot while on the monorail.

Either way, you'll have a great time!
Happy planning!!!!!!
