I hope you've got parental controls on the computers (including their own personal devices) and Netflix etc.....Boredom at home plus computers and unrestricted TV access equals a lot of opportunity for problems....
It sounds like they both need more to do. It's too bad that scout camps are probably already full because the boy could do more of them -- they are not limited to one per summer, are they? Same with cheer camps. Since they both liked those activities, have you checked into similar ones? They might be full, but there are cancellations at times.
I would have a roster of chores to be done, with some appropriate and substantial rewards for chores that are outside the usual "has to be done for everyday life" needs. If you want the garage cleaned out, the pantry reorganized, some furniture repainted, whatever, let them sit down with you and plan it, let them make their equipment or supply lists if needed, let them create a schedule for doing it. And PAY them for it. Like I said -- taking out the trash, cleaning the bathrooms, doing laundry etc. -- stuff that must be done by people to keep a household running -- those dont' get cash, but there is nothing wrong with paying older kids to do larger projects. Cash is a big incentive at their ages. And if you take these tasks seriously by asking them to write out their schedule and supply needs, and write down what you will pay and what constitutes a completed job, then they will learn responsibility and organization while you get a project done and they make some money. Just don't TELL them they are learning anything! My child is 13 and will make money this summer doing some big clear-outs and reorganizations of the pantry, kitchen cabinets and linen closet, all for pay.
At their ages I would not be very comfortable with kids just lounging around all day (despite a tendency on MP to believe kids are fine just "being kids") and hanging out). Do they have summer assignments for school? By middle school here, there are summer math packets to complete and hand in on the first day of school, and summer reading lists as well. They should do those -- if you are not aware whether their private school has such assignments, check with the school directly. The kids may not know there are assignments online they're supposed to check out and complete!
They can be unpaid summer pages at the local libraries (these "jobs" aren't paid but provide service hours that many schools require, even from younger teens). The 13-year-old may be old enough to volunteer at the local recreation center in some of its summer programs, and both kids are old enough to be dropped off for recreation center summer programs that are far cheaper than many camps. Have you checked out what the rec centers and community centers offer? They sometimes have tween and teen activities aimed at kids who are not in camps -- one-time events or movies during the day or short-term courses in lots of things, and usually not very expensive.