About 60% of cities I've read about have strict codes on residential exterior art, which can include garage doors. It's a shame your family's expression project got caught in that bureaucracy. In my experience, sometimes if you frame it as a temporary art installation or get a permit retroactively, there might be leeway, but take that with a grain of salt. Hoping you find a way to preserve that mural, or at least the spirit of it with your kids.
C'mon, is a painted garage door really that serious? Most code enforcement is complaint-driven, so unless a neighbor called it in, why would they even notice? I've seen way worse violations like unpermitted sheds that get ignored for years. It's just paint, not a structural change, so the bureaucracy seems overblown.
Honestly, that "freedom of expression" mural getting covered up is just plain ridiculous. Tbh, my family painted our fence with rainbows and the city called it a "visual disturbance." It really kills the fun of doing something creative with your kids.