I purchased a tie-dyed sarong at the gift shop outside the PoC that i use to drape over the double stroller when they are sleeping or i want them to just rest. Then I use it as a cute sarong round the pool. Any light weight fabric would work- you just don't want to carry a lot with you.
I also have taken towels from the hotel to roll up as a pillow, wipe off spills or dry the stroller off if it rains.
During our last trip, I went to JoAnn Fabrics and purchased 1 yd. of Buzz Lightyear fleece to use as a blanket for my young toddler and it was only $5. That way if it was lost I wouldn't care.