Welcome back, Leah! I've been on Disney's cruise ships during the height of the summer and during school in the winter, and neither time have I felt overwhelmed with crowds. There are definitely more children and families traveling during spring break (though spring breaks vary with different schools) and summer as well as major holidays, than during January and February.
Disney Cruise Line does an amazing job with offering such a wide variety of activities and events throughout the ship that rarely, with few exceptions, are the majority of guests all in one spot. The only time I really notice large crowds is during the
Sail Away party on the pool deck as we sail away from the port the very first afternoon. Most guests are up there celebrating the beginning of a magical vacation, and it certainly is crowded there. Again, on
Pirate Night, you'll notice crowds since most guests want to take part in the festivities on the pool deck for the Pirates IN the Caribbean party.
Other than those two events, you'll find that even if the ship is at capacity, you'll be interested in one activity, while other guests are off at another. I have never personally found the crowds to be too difficult.
My best advice would be to sail when it is best for your family's schedule. Whether that be during spring break or summer break or pulling the kids out of school for a week during the winter. No matter when you sail, you're sure to have an amazing time with Disney. Your grandkids are so lucky to get to set sail with their grandmother and Captain Mickey Mouse!
Please let me know if I can help with anything else as you continue to plan, Leah!