How old are your kids? If they're still young (like under 10), I'd help your kids tie dye the sheets, then sew ties on the ends. Easy, pretty tent material. Like giant play silks. I would have loved it if our bed sheets had had ties for us to attach them to chairs and such.
If they are still durable and no holes, you can back a quilt with them. I would be more likely to use one for throw quilts, not the keepsake kind, because the back will wear out before the top. You could still dye them and then put them on the back, but you have to be sure they won't bleed onto your top. Kymberli