That room just sounds really bright and garish to me...
What I would do, is pick out one or two of the colors that you really like, and let them be... then drape the other 3 walls with curtains or fabric in a more neutral, but light, color (maybe white or light grey). Would the family mind if you hung some curtain rods or knobs?
If they do decide to let you repaint the room as long as you paint it back, I'd still do the same thing - pick out one or two colors that you like and repaint the rest. It'll add color without being overwhelming, and it'll be less work when you have to restore it
