I love to do this same thing in the bathroom...I have my normal shower curtain, but then added another rod up high and hung two pulled back curtains on either side to frame the tub. (makes the bathroom seem SO much larger that way!!)
Instead of using the old mini blind slats, hand sew small plastic rings to the places where the slats above have their holes. Thread the mini-blind string through the rings and tie at the bottom ring. OR glue/sew pockets using add'l liner fabric to hide slats. See PureOfFaith.blogspot.com in favorites.