I have an 11yo and a 14yo. As you say, it's a challenge! We're not out in the sticks but I don't have much time off work and exH is as about as useful as a chocolate teapot.
This is our summer schedule:
Week 1: 11yo at a summer school run by the new high school she's attending from September. 14yo was supposed to be at a football camp but he's got COVID, so is in his room on his laptop and eating his way through the fridge instead.
Week 2: family holiday.
Week 3: 14yo at a residential football camp. 11yo will be coming with me to drop him off/pick him up, then has a riding camp on two other days.
Week 4: both off to stay with my parents and be spoiled for a week.
Week 5: 11yo riding camp x 2 days. 14yo entertaining himself. BH weekend in the West Country.
Week 6: 14yo at football camp x 4 days. 11yo at riding camp x 2 days.
I've signed 14yo up for a summer membership at the local gym. A few of his mates are also signed up, so I'm sure they'll head over a few times a week. £30 for 6 weeks unlimited gym, swim and classes - absolute bargain!