Arches and Canyonlands are best visited from Moab. There are lots of hotels in the town, Many with swimming pools. We stated at the Best Western Canyonlands last time, in a big suite (a free upgrade) that would accommodate your family very well. But I see the Gonzo Inn has a larger pool, and we might try that next time.
Hint: I use Google maps satellite view to check out features like pool size, trees or gardens on the property, etc.
For Zion, we find the best place to stay in in the town of Springdale, right at the entrance gate. There is a nice national parks lodge inside the park, but it is likely full, and they do not have a pool.
We like the Desert Pearl, but if that is above your budget, there are the usual chain hotels like Springhill Suites, Hampton Inn, and Holiday Inn Express, all with pools, and the newly-renovated Lodge at Zion Country which is new to me.
for Grand Canyon South Rim, I highly recommend staying inside the park. There are four lodges lined up right on the rim of the canyon—-walk out the door and you are there. These range in price from the budget Bright Angel Lodge (which to my recollection has no rooms to accommodate a family of 4) to the pricy El Tovar, with the motel-like Thunderbird and Kachina Lodges in between. These latter 2 have rooms with 2 queen beds to sleep 4 but do not allow an extra bed. Maswik Lodge is an additional lodge back from the rim, which often has rooms when the rim lodges are booked. I believe they will allow a rollaway in a 2-queen room if you need separate beds for the teens.
Book these on the official website:
https://www.grandcanyonlodges.com/
Your best option might be Yavapai Lodge, which is run by another company. They have tru “family rooms” with a queen bed and a set of bunks. Book on their website:
https://www.visitgrandcanyon.com/stay/lodging/yavapai-lodge/
Capitol Reef is tough; we have not stayed in anyplace I would recommend there. But we have avoided the high-end lodges there, and perhaps one of those will suit. It is a beautiful park, less crowded than the others.
None of these lodges inside the park offer pools, but with the elevation at the rim being 7000 feet it is not nearly as hot as the other parks. However, if a pool is a “must”, then look in the town of Tusayan outside the park entrance.