I love camping and would happily sleep in a tent for 3 weeks.
Things to consider: it may take your kids 2 weeks to get used to sleeping past bright sunlight at 5am. There are tents with good ‘blackout’ sleeping pods, but not pretty canvas bell tents.
What makes the ‘luxury’ of glamping type tents is the sleeping arrangements provided. Sleep comfort is essential. Some people are perfectly comfortable on blow up beds, if that’s you, no problem,
I like a SIM, and for 3 weeks a good thick one. £70 minimum! The kids can manage in thinner, cheaper one though: less weight so don’t need as much depth to keep them off the floor.
Would the children be happy to go to bed in the tent while you socialise indoors? (My eldest slept in his own tent when we camped from age 9 and youngest would be ok with eldest). Or if you are sitting out in the garden talking during those lovely summer evenings, will the kids sleep? No sound insulation in a tent.
Same consideration if they live on a noisy road.
But maybe you are all fine with kids staying up til dark and then eventually sleeping in.
What about hiring a caravan? If it could be parked on the garden? I had a quick look at a company called Camptoo that rents caravans, and a big luxurious caravan for 3 weeks soon was £45 a night. You get a chemical toilet in a caravan!