Hi Kristen!
If you have a chance to stay at
Disney's Grand Floridian Resort & Spa, I highly recommend doing it. My family stayed there last year and I also spend a week there for a conference just in December. It's such a beautiful resort and my kids had a blast in the pools. The location is ideal just being a monorail ride or a ferry boat ride away from the Magic Kingdom.
Having a split stay is a great idea. This allows you to experience two totally different resorts during the same vacation. We love
Disney's Caribbean Beach Resort because of the pool. My kids got a kick out of the pirate rooms. You can easily have your luggage transferred from one resort to the other.
Another resort you should look into is
Disney's Coronado Springs Resort if you're thinking about a moderate as your second resort stay. Since you mentioned you've stayed at Caribbean Beach many times, why not try two new resorts! This resort has a Southwestern flare and circles a beautiful lake. I love everything about this resort right down to the sliding wood doors that separate the bedroom from the bathroom. The details in everything are amazing.
If you are booking Walt Disney World vacation packages, you would need to book them as two separate packages.
Have a magical day!
Leslie