Do you have a reasonably good relationship with the mom? If so, then by all means tell her. If not, bear in mind that, if you tell her her kid's a klutz and is destroying your house, she may get her nose out of joint and decide your kid's a brat and her little one shouldn't play with her anymore.
Since you can't just pick up banana oil at the corner market, sending the bed skirt to the cleaners is probably the only way you'll be able to get the polish out. And, if a rental steam carpet cleaner does not get the mess out of the carpet, you may have to hire a professional cleaner to come in and take care of the carpets. But a delicate way of broaching the subject to your daughter's friend's mom is, just in passing conversation, ask Mrs. Louhoo if she knows anything short of a professional cleaner that will get nail polish out of fabric. When she asks what happened, and she will, just mention that little Cindy and your daughter were playing and Cindy Louhoo spilled nail polish on the bedskirt and floor. Hopefully, at that point, she will have enough integrity to offer to pay (at least half) the cost of the cleaning bill. If not, it's okay to go ahead and get the job done then take the bill to her. "You seemed so upset over Cindy's accident and I just wanted to let you know I got it taken care of. Here's the bill."
One question, though. How old are these girls? Pre-teens? Younger?
If they are younger than nine, they probably need to be monitored very closely and not left alone for longer than a few minutes at a time. If they want to get into the nail polish, quickly provide them with newspaper or something to cover expensive furniture or carpeting. If they are nine or older, it's time they take responsibility for their own actions. Let Little Miss Cindy Louhoo pay for at least part of the cleaning bill. If she babysits, she can pay you a portion of that each week until your agreed-upon payback price is reached. You will not only be helping to pay the cleaning bill, but you will be teaching Cindy and your daughter a valuable lesson in responsibility and owning up to one's own actions. And THAT should make them both more cautious in the future.
Barbara is quite correct in saying, when the girl is at your house, she is your responsibility. It's okay to set down rules for both girls and insist they follow them.