I’ve never been to WDW in the summer, but I would assume it’s more difficult to get chairs then, as opposed to when we go in January/February.
Last time we were at AKL in late January to early February. This did not align with a federal holiday, school break, or as far as I could tell, any other big draw. Both the main hotel pool and the pool at Kidani were pretty full of people in chairs, or at least the chairs that are “taken” by a towel all day. Few minutes of looking and we were always successful getting at least a pair somewhere.
This most recent time, we went around Presidents’ Day. Few days before the holiday we were at Saratoga Springs’ paddock pool. Were only able to get the farthest back (sub-optimal) bistro table to the side of the paddock grill, basically 4’ from the door the employees go in and out of.
The rest of the trip, we were at Wilderness lodge, where the main pool was madness and chairs were “all taken” (again, many by just towels for hours on end), such that over the course of 4 or so attempts, we only got a pair of chairs once, not even by the pool, but by the kiddie splash area. The pool at boulder ridge was always easy to find a table and/or lounge chairs.