While I think it's rude to expect you to provide towels, and I'd make sure my children took their own if we were invited to use your pool, I don't think 10 extra beach towels a week qualifies as that much "extra" laundry, really. And honestly, a load or two of towels is about as easy as it gets for laundry. You don't even have to fold them if you don't want to.
I'd be teaching some children how to run the washer and dryer, and I'd tell them they could swim while the towels were being washed, then they could transfer them to the dryer and swim some more until time to fold them and put them away. I'd either teach the "regular" visitors or I'd use it as a time to teach my own children how to run the washing machine. If kids are old enough to be coming over without parents to swim, they're old enough to use the washer and dryer, with supervision of course.
Just my opinion...