No experience with my own kids, but I moved from a local public school to Paul VI Caltholic school 2nd semester junior year. It was much easier than I expected it to be - the kids were curious about me so it was pretty easy to make new friends. It also felt like a clean start, which I needed at the time, so it helped make things easier. The move was my choice, but if this is not your DC choice you'll likely have a more difficult time. Good luck!