Hi Alexandra,
My family has booked two different Walt Disney World Resorts and we never had any issues.
On the last day of your stay at your first resort, call bell services and have them pick up and deliver your luggage to your new resort. You can then head to a park,
water park or
Disney Springs for the day and return to your new resort later.
Once you arrive at your new resort, bell services will grab your bags and deliver them to your room.
The only reason for you to head to your new resort before heading out for the day would be if you are on the Disney Dining plan which needs to be activated at your resort. In this case, the easiest way to get there is to call an Uber car or a taxi. Otherwise, you would have to go to a park or Disney Springs as a transfer hub.
Wishing you a magical vacation!
Beth