Would a rod stick out enough to go over the molding and sill, or would curtains look kind of bent where they hang over the molding? Personally, I love plain white linen curtains like your last picture. Another option, light filtering shades, http://www.ikea.com/us/en/catalog/products/70314592/ However, they don't offer complete privacy at night.

Try some roman shades on the windows, wicker/woven type of look. Rug is too small for the room really, so if you can upgrade to something larger, I would. Nesting tables can be kid friendly, and there are many that won't break the bank, look into some of those until your kids are old enough for a nicer table. I saw this really cute idea for a kid friendly coffee table on Houzz, paired with little kid chairs. Super cute, very practical. You have the space, I think you need something there definitely.https://www.houzz.com/photos/kid-friendly-coffee-table-phbr0lbl-bl~l_4341

I see no relationship between the blue walls and anything else in the room and if the drapes had blue and cream or beige stripes that might solve the problem. The room is very linear and a large green plant and a round or oval centerpiece would help to correct that.

I would not use brown blinds.....they are very cavelike. You could use white cafe curtains on rings. They could be closed after dark but kept open during the day. They are a very sweet look, too.