Shutters would be a great solution, especially since you mentioned kiddos sleeping. The larger the individual louver (slat, if you will), the more of your view you will be preserving when they are fully tilted open in the horizontal position. In my experience, most people don't open their shutters except to clean their windows. But of course the option is always there. Shutters can also be magnetized to the frame for some openings that aren't too large. If you choose to go with shutters, you will never have to think about your windows again. Consider it done. I personally love them, especially for windows that are unusually shaped such as yours.

Interior shutters are made out of either wood, Vinly or faux wood. Wood being the most expensive and vinyl being the least.There are so many different mfg it will make your head spin. I do know that you will save a considerable amount of money buy buying online. I install shutters and blinds for a living. When I was in the market last year for 2 shutters I first checked with The companies I install for and with a employee discount I still saved 50% by buying online of the exact same mfg. The company I used was normal shutters.I would suggest you have them professionally measured and installed.

Your place is more MCM than you let on! I have seen photos somewhere of a solution to this. But for the life of me, I can't remember where. What the person had done was: make a cutout the shape of the window out of something substantial but not too heavy -- maybe a piece of lauan wood or oysterboard/foamcore? Then it was hung in front of the window on hook eyes or something. Then a string was attached to it, and run up to the ceiling through an eye and then down to where it could be secured on one of those little cleats on the wall. That way the string could be pulled and it would pull the cover "up" to allow the light in. But most of the time it just hung in front of the window. It could be painted the color of the blinds below, or you could take the opportunity to put a graphic on it that the kids might like.

Definitely light white or off white. Dark shutters block your view, visually your eye stops at the dark shutter but not a light color. It appears the room would be too dark with dark shutters.