Greetings Michelle!
I am beyond thrilled that you are planning a once-in-a-lifetime Disney vacation! As someone who frequents both Walt Disney World and Disneyland Resorts throughout the year, this is a tough call as both are so unique and fun in my opinion!
The Disneyland Resort is full of charm and history with the park that started it all! It is also home to detailed themed lands like Cars Land in Disney California Adventure Park. Timeless classic attractions like the original Pirates of the Caribbean and "it's a small world" at Disneyland Park are also not-to-be-missed. The proximity of the two theme parks of this Resort make park hopping throughout the day a breeze. You can also easily walk back to your Disneyland Resort Hotel room to enjoy the great pools or take an afternoon nap!
Walt Disney World Resort is truly a whole new world! With four distinct parks, many themed resort hotels, and
Disney Springs, there are endless adventures to be had! The Walt Disney World Resort is home to stunning Pandora - the World of Avatar featuring the most exquisite and technologically advanced theming and attractions. You can also take a virtual world tour with a stroll through Epcot's World Showcase to experience the sights, sounds, and tastes of 11 different countries. With so much to experience and explore at the Walt Disney World Resort, I highly recommend visiting for at least one full week, especially if it is your only visit.
With four days allotted for your trip, you may have a more satisfying and also relaxing vacation at the Disneyland Resort. This Resort also has an abundance of character experiences which you said is a priority for your family. There is no wrong time to visit, but crowds tend to be lighter in the fall and winter when school is in session.
I hope this was helpful, and feel free to stop by again as you start planning your trip!
-Jennifer