Hi Laura!
Your travel time is in that in-between state. At the start of your vacation (the 15th), you'll definitely beat the rush as most U.S. school children don't get out till around the 17th. After the 17th, it will pick up each day till about the 26th, tamper off somewhat to the 29th, then pick up again the 30th, 31st, and the new year.
But, it is significantly busier the 21st-26th then the 15th-20th, so, in those terms, you will be beating the major Christmas rush..
As for the Mickey's Very Merry Christmas Party, our family starts at the top of Main Street for the Christmas Parade, then we make our way up to Cinderella's Castle for the Holiday Wishes fireworks show. We'll then make our way towards Frontier Land, then Liberty Square, Fantasy Land, and try to work our way around back to Main Street.
Have a terrific time with the family at Disney!